Nonlinear Potential Theory

People with whom we collaborate or have close contacts with include the following people.

Sylvester Eriksson-Bique at University of Oulu
Stephen Gardiner at University College Dublin
Ugo Gianazza at University of Pavia
Agnieszka Kałamajska at Warsaw University
Juha Kinnunen and Riikka Korte at Aalto University, Helsinki
Visa Latvala at University of Eastern Finland, Joensuu
Juha Lehrbäck and Mikko Parviainen at Jyväskylä University
Xining Li at Sun Yat-sen University, Guangzhou (Canton)
Olli Martio and Xiao Zhong at Helsinki University

The list below contains the mathematical publications (in reverse chronological order) of the members of the group.

Books

A. Björn and J. Björn, Nonlinear Potential Theory on Metric Spaces, EMS Tracts in Mathematics 17, European Mathematical Society, Zürich, 2011, 415 pp., ISBN 978-3-03719-099-9. Distributed by EMS and AMS. Corrections and clarifications (last updated 3 May 2018).
The authors' profit from the book above is donated to Barndiabetesfonden (The Swedish Child Diabetes Fund).
A. Asratian, A. Björn and B. O. Turesson, Diskret Matematik, Liber, Stockholm, 2020, 344 pp. (Swedish).

Ph.D. theses

A. Mwasa, Boundary Value Problems for Nonlinear Elliptic Equations in Divergence Form, Ph.D. Dissertation, Linköping Studies in Science and Technology. Dissertations No. 2128, Linköping, 2021, 115 pp. (supervisors Anders Björn, Jana Björn, Tomas Sjödin).
It consists of the following three papers:
Mixed boundary value problem for p-harmonic functions in an infinite cylinder (with J. Björn), Nonlinear Anal. 202 (2021), 112134. 30 pp. doi:10.1016/j.na.2020.112134 Journal (Open choice), arXiv
Resolutivity and invariance for the Perron method for degenerate equations of divergence type (with A. Björn and J. Björn), arXiv
Behaviour at infinity for solutions of a mixed nonlinear elliptic boundary value problem via inversion (with J. Björn), arXiv (This version is slightly different from the version printed in the dissertation.)
L. Malý, Sobolev-Type Spaces: Properties of Newtonian Functions Based on Quasi-Banach Function Lattices in Metric Spaces, Ph.D. Dissertation, Linköping Studies in Science and Technology. Dissertations No. 1591, Linköping, 2014, 168 pp. (supervisors Anders Björn, Jana Björn, Tomas Sjödin).
It consists of the following four papers (the links here are to slightly different arXiv versions):
Newtonian spaces based on quasi-Banach function lattices (this paper will appear in Math. Scand.),
Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices (this paper has appeared in Ann. Acad. Sci. Fenn. Math. 38 (2013), 727-745),
Regularization of Newtonian functions on metric spaces via weak boundedness of maximal operators,
Fine properties of Newtonian functions and the Sobolev capacity on metric measure spaces.
Z. Farnana, The Double Obstacle Problem on Metric Spaces, Ph.D. Dissertation, Linköping Studies in Science and Technology. Dissertations No. 1283, Linköping, 2009, 94 pp. (supervisors Jana Björn, Anders Björn, Lars-Erik Andersson).
T. Sjödin, Topics in Potential Theory: Quadrature Domains, Balayage and Harmonic Measure, Doctoral Thesis in Mathematics, TRITA-MAT-05-MA-05, Royal Institute of Technology, Stockholm, 2005, 232 pp. (supervisor Björn Gustafsson).
J. Björn, Interior Regularity and Boundary Behaviour of Solutions to Second Order Elliptic Equations, Ph.D. Dissertation, Linköping Studies in Science and Technology. Dissertations No. 446, Linköping, 1996, 92 pp. (supervisor Vladimir Maz'ya).
A. Björn, Removable Singularities for Hardy Spaces of Analytic Functions, Ph.D. Dissertation, Linköping Studies in Science and Technology. Dissertations No. 365, Linköping, 1994, 74 pp. (supervisor Lars Inge Hedberg).

Licentiate theses

A. Christensen, Capacities, Poincaré Inequalities and Gluing Metric Spaces, Licentiate thesis, Linköping Studies in Science and Technology. Theses. No. 1961, Linköping, 2023, 60 pp. ArXiv versions of the include paper is available here Poincaré inequalities and A_p weights on bow-ties (supervisors Anders Björn, Jana Björn, Tomas Sjödin).
L. Malý, Newtonian Spaces Based on Quasi-Banach Function Lattices, Licentiate thesis, Linköping Studies in Science and Technology. Theses. No. 1543, Linköping, 2012, 60 pp. ArXiv versions of the two papers are available here Newtonian spaces based on quasi-Banach function lattices and Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices (supervisors Anders Björn, Jana Björn, Tomas Sjödin).
Z. Farnana, The Double Obstacle Problem on Metric Spaces, Licentiate thesis, Linköping Studies in Science and Technology. Theses. No. 1342, Linköping, 2008, 52 pp. (supervisors Jana Björn, Anders Björn, Lars-Erik Andersson).
A. Björn, Removable singularities of H^p-spaces in plane domains, Licentiate thesis, Linköping Studies in Science and Technology. Theses. No. 287, Linköping, 1991, 23 pp. (supervisor Lars Inge Hedberg).

For Master's and Bachelor's theses see the bottom of this page.

Preprints

G. Baravdish, G. Eilertsen, R. Jaroudi, B. T. Johansson, L. Malý and J. Unger, Learning via nonlinear conjugate gradients and depth-varying neural ODEs, Preprint, 2022. arXiv
A. Björn, J. Björn and M. Kim, Perron solutions and boundary regularity for nonlocal nonlinear Dirichlet problems, Preprint, 2024. arXiv
A. Björn, J. Björn, R. Korte, S. Rogovin and T. Takala, Preserving Besov (fractional Sobolev) energies under sphericalization and flattening, Preprint, 2024. arXiv
A. Björn, J. Björn and V. Latvala, The Perron method associated with finely p-harmonic functions on finely open sets, Preprint, 2022. arXiv
J. Björn and A. Mwasa, Behaviour at infinity for solutions of a mixed boundary value problem via inversion, Preprint, 2021. arXiv
R. Jaroudi, L. Malý, G. Eilertsen, B.T. Johansson, J. Unger and G. Baravdish, Standalone Neural ODEs with Sensitivity Analysis, Preprint, 2022. arXiv
L. Malý, Trace and extension theorems for Sobolev-type functions in metric spaces, Preprint, 2017. arXiv

Refereed articles

To appear
A. Björn, J. Björn and V. Latvala, The Perron method associated with finely p-harmonic functions on finely open sets, to appear in Potential Anal. arXiv

2024
A. Björn and J. Björn, Condenser capacities and capacitary potentials for unbounded sets, and global p-harmonic Green functions on metric spaces, Comm. Partial Differential Equations 49 (2024), 938-988. doi:10.1080/03605302.2024.2411521 Journal (Open choice) arXiv
A. Björn, J. Björn and A. Christensen, Poincaré inequalities and A_p weights on bow-ties, J. Math. Anal. Appl. 539 (2024), Paper No. 128483, 28 pp. doi:10.1016/j.jmaa.2024.128483 Journal (Open choice) arXiv
J. Björn, A Wiener criterion for the fractional Laplacian, Proc. Amer. Math. Soc. 152 (2024), 1053-1065. doi:10.1090/proc/16647 Journal arXiv
D. Manolis, On the Problem of Integrating Infinite Derivatives, Real Anal. Exchange 49 (2024), 293-298. doi:10.14321/realanalexch.1.1.1685253661 Journal

2023
R. Alvarado, P. Hajłasz and L. Malý, A simple proof of reflexivity and separability of N^1,p Sobolev spaces, Ann. Fenn. Math. 48 (2023), 255-275. doi:10.54330/afm.127419 Journal (Open access), arXiv
A. Björn and J. Björn, Sharp Besov capacity estimates for annuli in metric spaces with doubling measures, Math. Z. 305 (2023), Paper No. 41, 26 pp. doi:10.1007/s00209-023-03360-0 Journal (Open choice) arXiv
A. Björn, J. Björn and P. Lahti, Removable sets for Newtonian Sobolev spaces and a characterization of p-path almost open sets, Rev. Mat. Iberoam. 39 (2023), 1143-1180. doi:10.4171/RMI/1419 Journal (Open access), arXiv
A. Björn, J. Björn and V. Latvala, The Dirichlet problem for p-minimizers on finely open sets in metric spaces, Potential Anal. 59 (2023), 1117-1140. doi:10.1007/s11118-022-09996-7 Journal (Open choice), arXiv
A. Björn, J. Björn and V. Latvala, Convergence and local-to-global results for p-superminimizers on quasiopen sets, J. Differential Equations 365 (2023), 812-831. doi:10.1016/j.jde.2023.05.009 Journal (Open choice), arXiv
A. Björn, J. Björn and J. Lehrbäck, Volume growth, capacity estimates, p-parabolicity and sharp integrability properties of p-harmonic Green functions, J. Anal. Math. 150 (2023), 159-214. doi:10.1007/s11854-023-0273-4 Journal (Open choice), arXiv

2022
A. Björn, Removable singularities for bounded A-(super)harmonic and quasi(super)harmonic functions on weighted Rⁿ, Nonlinear Anal. 222 (2022), Paper No. 112906, 16 pp. doi:10.1016/j.na.2020.112907 Journal (Open choice), arXiv
A. Björn, J. Björn and A. Mwasa, Resolutivity and invariance for the Perron method for degenerate equations of divergence type, J. Math. Anal. Appl. 509 (2022), Paper No. 125937, 14 pp. doi:10.1016/j.jmaa.2021.125937 Journal (Open choice), arXiv
A. Björn, J. Björn and N. Shanmugalingam, Extension and trace results for doubling metric measure spaces and their hyperbolic fillings, J. Math. Pures Appl. 159 (2022), 196-249. doi:10.1016/j.matpur.2021.12.003 Journal (Open choice), arXiv, Preprint CVGMT
A. Björn, J. Björn and N. Shanmugalingam, Classification of metric measure spaces and their ends using p-harmonic functions, Ann. Fenn. Math. 47 (2022), 1025-1052. doi:10.54330/afm.120618 Journal (Open access), arXiv, Preprint CVGMT
A. Björn and D. Hansevi, Semiregular and strongly irregular boundary points for p-harmonic functions on unbounded sets in metric spaces, Collect. Math. 73 (2022), 253–270. doi:10.1007/s13348-021-00317-6 Journal (Open choice), arXiv
J. Björn and A. Kałamajska, Poincaré inequalities and compact embeddings from Sobolev type spaces into weighted L^q spaces on metric spaces, J. Funct. Anal. 282 (2022), Paper No. 109421, 47 pp. doi:10.1016/j.jfa.2022.109421 Journal (Open choice), arXiv
S. J. Gardiner and T. Sjödin, On a conjecture of Gustafsson and Lin concerning Laplacian growth, Anal. Math. Phys. 12 (2022), Paper No. 38, 9 pp. doi:10.1007/s13324-022-00647-z Journal (Open choice),
S. J. Gardiner and T. Sjödin, Boundary points of angular type form a set of zero harmonic measure, Ann. Fenn. Math. 47 (2022), 641-644. doi:10.54330/afm.116146 Journal (Open access),

2021
A. Björn, J. Björn and N. Shanmugalingam, The Liouville theorem for p-harmonic functions and quasiminimizers with finite energy, Math. Z. 297 (2021), 827-854. doi:10.1007/s00209-020-02536-2 Journal (Open choice), arXiv
A. Björn, J. Björn and N. Shanmugalingam, Bounded geometry and p-harmonic functions under uniformization and hyperbolization, J. Geom. Anal. 31 (2021), 5259-5308. doi:10.1007/s12220-020-00477-0 Journal (Open choice), arXiv
J. Björn and A. Mwasa, Mixed boundary value problem for p-harmonic functions in an infinite cylinder, Nonlinear Anal. 202 (2021), Paper No. 112134, 30 pp. doi:10.1016/j.na.2020.112134 Journal (Open choice), arXiv

2020
A. Björn and J. Björn, A uniqueness result for functions with zero fine gradient on quasiconnected sets, Ann. Sc. Norm. Super. Pisa Cl. Sci. 21 (2020), 293-301. doi:10.2422/2036-2145.201802_014 Journal, arXiv
A. Björn, J. Björn and J. Lehrbäck, Existence and almost uniqueness for p-harmonic Green functions on bounded domains in metric spaces, J. Differential Equations 269 (2020), 6602-6640. doi:10.1016/j.jde.2020.04.044 Journal (Open choice), arXiv
A. Björn, J. Björn and I. Mirumbe, The quasisuperminimizing constant for the minimum of two quasisuperminimizers in Rⁿ, Ann. Acad. Sci. Fenn. Math. 45 (2020), 215-225. doi:10.5186/aasfm.2020.4508 pdf, Journal (Open access), arXiv
A. Björn, J. Björn and N. Shanmugalingam, Locally p-admissible measures on R, J. Funct. Anal. 278 (2020), Paper No. 108344, 17 pp. doi:10.1016/j.jfa.2019.108344 Journal, arXiv
S. J. Gardiner, M. Ghergu and T. Sjödin, Isoperimetric inequalities for Bergman analytic content, Indiana Univ. Math. J. 69 (2020), 1231-1249. doi:10.1512/iumj.2020.69.7898 Journal, Preprint
S. J. Gardiner and T. Sjödin, On a conjecture of Král concerning the subharmonic extension of continuously differentiable functions, Math. Bohem. 145 (2020), 71-73. doi:10.21136/MB.2019.0104-18 Journal (Open access)

2019
A. Björn, The Kellogg property and boundary regularity for p-harmonic functions with respect to the Mazurkiewicz boundary and other compactifications, Complex Var. Elliptic Equ. 64 (2019), 40-63. doi:10.1080/17476933.2017.1410799 Journal, arXiv. (For a free eprint copy (there are 50 in total), type "https://www.tandfonline.com/" followed by "eprint/ZiXIdChA5GADua7jmqK6/full". Please report to me if this doesn't work.) Correction, ibid. 64 (2019), 1756-1757. doi:10.1080/17476933.2018.1551890 Journal (Open choice, correction only). (The arXiv version contains the correction at the end.)
A. Björn and J. Björn, Poincaré inequalities and Newtonian Sobolev functions on noncomplete metric spaces, J. Differential Equations 266 (2019), 44-69. doi:10.1016/j.jde.2018.07.029 Journal (Open access), arXiv Corrigendum, ibid. 285 (2021), 493-495. doi:10.1016/j.jde.2021.03.008 Journal (Open choice). (The arXiv version contains the corrigendum at the end.)
A. Björn, J. Björn and X. Li, Sphericalization and p-harmonic functions on unbounded domains in Ahlfors regular metric spaces, J. Math. Anal. Appl. 474 (2019), 852-875. doi:10.1016/j.jmaa.2019.01.071 Journal (Open access), arXiv
A. Björn, J. Björn and M. Parviainen, The tusk condition and Petrovskii criterion for the normalized p-parabolic equation, J. Lond. Math. Soc. 100 (2019), 623-643. doi:10.1112/jlms.12224 Journal, arXiv
A. Björn and D. Hansevi, Boundary regularity for p-harmonic functions and solutions of obstacle problems on unbounded sets in metric spaces, Anal. Geom. Metr. Spaces 7 (2019), 179-196. doi:10.1515/agms-2019-0009 Journal (Open access), arXiv
S. J. Gardiner and T. Sjödin, A characterization of annular domains by quadrature identities Bull. Lond. Math. Soc. 51 (2019), 436–442. doi:10.1112/blms.12243 Journal
P. Lahti, L. Malý, N. Shanmugalingam and G. Speight, Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient, J. Geom. Anal. 29 (2019), 3176-3220. doi:10.1007/s12220-018-00108-9 Journal, arXiv, Preprint CVGMT

2018
H. Aikawa, A. Björn, J. Björn and N. Shanmugalingam, Dichotomy of global capacity density in metric measure spaces, Adv. Calc. Var. 11 (2018), 387-404. doi:10.1515/acv-2016-0066 Journal, arXiv, Preprint CVGMT
A. Björn and J. Björn, Local and semilocal Poincaré inequalities on metric spaces, J. Math. Pures Appl. 119 (2018), 158-192. doi:10.1016/j.matpur.2018.05.005 Journal (Open access), arXiv
A. Björn and J. Björn, Tensor products and sums of p-harmonic functions, quasiminimizers and p-admissible weights, Proc. Amer. Math. Soc. 146 (2018), 5195-5203. doi:10.1090/proc/14170 Journal (Open access), arXiv
A. Björn, J. Björn, U. Gianazza and J. Siljander, Boundary regularity for the porous medium equation, Arch. Ration. Mech. Anal. 230 (2018), 493-538. doi:10.1007/s00205-018-1251-3 Journal (Open choice), arXiv
A. Björn, J. Björn and V. Latvala, The Cartan, Choquet and Kellogg properties for the fine topology on metric spaces, J. Anal. Math. 135 (2018), 59-83. doi:10.1007/s11854-018-0029-8 Journal (Open choice), Preprint Institut Mittag-Leffler no. 41 (40), 2014. arXiv
A. Björn, J. Björn and T. Sjödin, The Dirichlet problem for p-harmonic functions with respect to arbitrary compactifications, Rev. Mat. Iberoam. 34 (2018), 1323-1360. doi:10.4171/RMI/1025 Journal (Open access), arXiv
S. J. Gardiner, M. Ghergu and T. Sjödin, Analytic content and the isoperimetric inequality in higher dimensions, J. Funct. Anal. 275 (2018), 2284-2298. Journal (Open access), arXiv
D. Hansevi, The Perron method for p-harmonic functions in unbounded sets in Rⁿ and metric spaces, Math. Z. 288 (2018), 55-74. doi:10.1007/s00209-017-1877-0 Journal (Open choice), arXiv
P. Lahti, L. Malý and N. Shanmugalingam, An analog of the Neumann problem for the 1-Laplace equation in the metric setting: existence, boundary regularity, and stability, Anal. Geom. Metr. Spaces 6 (2018), 1-31. doi:10.1515/agms-2018-0001 Journal (Open access), arXiv
L. Malý, Regularization of Newtonian functions on metric spaces via weak boundedness of maximal operators, J. Anal. Math. 134 (2018), 1-54. doi:10.1007/s11854-018-0001-7 Journal, arXiv
L. Malý and N. Shanmugalingam, Neumann problem for p-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity, J. Differential Equations 265 (2018), 2431-2460. doi:10.1016/j.jde.2018.04.038 Journal (Open access), arXiv, Preprint CVGMT
L. Malý, N. Shanmugalingam and M. Snipes, Trace and extension theorems for functions of bounded variation, Ann. Sc. Norm. Super. Pisa Cl. Sci. 18 (2018), 313-341. doi:10.2422/2036-2145.201511_007 Journal (Open access), arXiv

2017
A. Björn, J. Björn and U. Gianazza, The Petrovskii criterion and barriers for degenerate and singular p-parabolic equations, Math. Ann. 368 (2017), 885-904. doi:10.1007/s00208-016-1415-0 Journal, arXiv
A. Björn, J. Björn, J. T. Gill and N. Shanmugalingam, Geometric analysis on Cantor sets and trees, J. Reine Angew. Math. 725 (2017), 63-114. doi:10.1515/crelle-2014-0099 Journal, arXiv
A. Björn, J. Björn and R. Korte, Minima of quasisuperminimizers, Nonlinear Anal. 155 (2017), 264-284. doi:10.1016/j.na.2017.02.003 Journal, arXiv
A. Björn, J. Björn and J. Lehrbäck, Sharp capacity estimates for annuli in weighted Rⁿ and in metric spaces, Math. Z. 286 (2017), 1173-1215. doi:10.1007/s00209-016-1797-4 Journal (Open choice), Preprint Institut Mittag-Leffler no. 17 (6), 2013. arXiv
A. Björn, J. Björn and J. Lehrbäck, The annular decay property and capacity estimates for thin annuli, Collect. Math. 68 (2017), 229-241. doi:10.1007/s13348-016-0178-y Journal, arXiv
A. Björn, J. Björn and J. Malý, Quasiopen and p-path open sets, and characterizations of quasicontinuity, Potential Anal. 46 (2017), 181-199. doi:10.1007/s11118-016-9580-z Journal (Open choice), arXiv

2016
J. Arnlind, A. Björn and J. Björn, An axiomatic approach to gradients with applications to Dirichlet and obstacle problems beyond function spaces, Nonlinear Anal. 134 (2016), 70-104. doi:10.1016/j.na.2015.12.010 Journal, arXiv
A. Björn, J. Björn and V. Latvala, Sobolev spaces, fine gradients and quasicontinuity on quasiopen sets, Ann. Acad. Sci. Fenn. Math. 41 (2016), 551-560. doi:10.5186/aasfm.2016.4130 pdf, Journal (Open access), arXiv
A. Björn, J. Björn and N. Shanmugalingam, The Mazurkiewicz distance and sets that are finitely connected at the boundary, J. Geom. Anal. 26 (2016), 873-897. doi:10.1007/s12220-015-9575-9 Journal, Preprint Institut Mittag-Leffler no. 14 (10), 2013. arXiv
J. Björn, Sharp exponents and a Wiener type condition for boundary regularity of quasiminimizers, Adv. Math. 301 (2016), 804-819. doi:10.1016/j.aim.2016.06.024 Journal (Open access), arXiv.
L. Malý, Newtonian spaces based on quasi-Banach function lattices, Math. Scand. 119 (2016), 133-160. doi:10.7146/math.scand.a-24188 Journal (Open access), arXiv
L. Malý, Fine properties of Newtonian functions and the Sobolev capacity on metric measure spaces, Rev. Mat. Iberoam. 32 (2016), 219-255. doi:10.4171/RMI/884 Journal (Open access), arXiv
T. Sjödin, A new approach to Sobolev spaces in metric measure spaces, Nonlinear Anal. 142 (2016), 194-237. doi:10.1016/j.na.2016.04.010 Journal, arXiv

2015
T. Adamowicz, The geometry of planar p-harmonic mappings: convexity, level curves and the isoperimetric inequality, Ann. Sc. Norm. Super. Pisa Cl. Sci. 14 (2015), 263-292. doi:10.2422/2036-2145.201201_010 Journal (Open access), Preprint
T. Adamowicz, P. Harjulehto and P. Hästö, Maximal operator in variable exponent Lebesgue spaces on unbounded quasimetric measure spaces, Math. Scand. 116 (2015), 5-22. doi:10.7146/math.scand.a-20448 Journal (Open access), Preprint
A. Björn, The Dirichlet problem for p-harmonic functions on the topologist's comb, Math. Z. 279 (2015), 389-405. doi:10.1007/s00209-014-1373-8 Journal, arXiv
A. Björn and J. Björn, Obstacle and Dirichlet problems on arbitrary nonopen sets, and fine topology, Rev. Mat. Iberoam. 31 (2015), 161-214. doi:10.4171/RMI/830 Journal (Open access), arXiv
A. Björn, J. Björn, U. Gianazza and M. Parviainen, Boundary regularity for degenerate and singular parabolic equations, Calc. Var. Partial Differential Equations 52 (2015), 797-827. doi:10.1007/s00526-014-0734-9 Journal, Preprint Institut Mittag-Leffler no. 4 (20), 2013, arXiv
A. Björn, J. Björn and V. Latvala, The weak Cartan property for the p-fine topology on metric spaces, Indiana Univ. Math. J. 64 (2015), 915-941. doi:10.1512/iumj.2015.64.5527 Journal, Preprint Institut Mittag-Leffler no. 5 (18), 2013. arXiv
A. Björn, J. Björn and N. Shanmugalingam, The Dirichlet problem for p-harmonic functions with respect to the Mazurkiewicz boundary, and new capacities, J. Differential Equations 259 (2015), 3078-3114. doi:10.1016/j.jde.2015.04.014 Journal (Open access), arXiv
D. Hansevi, The obstacle and Dirichlet problems associated with p-harmonic functions in unbounded sets in Rⁿ and metric spaces, Ann. Acad. Sci. Fenn. Math. 40 (2015), 89-108. doi:10.5186/aasfm.2015.4005 pdf, Journal (Open access), arXiv

2014
T. Adamowicz, Phragmen-Lindelöf theorems for equations with nonstandard growth, Nonlinear Anal. 97 (2014), 169-184. doi:10.1016/j.na.2013.11.018 Journal, Preprint
T. Adamowicz, A. Björn and J. Björn, Regularity of p(·)-superharmonic functions, the Kellogg property and semiregular boundary points, Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), 1131-1153. doi:10.1016/j.anihpc.2013.07.012 Journal (Open access), arXiv
A. Björn and J. Björn, The variational capacity with respect to nonopen sets in metric spaces, Potential Anal. 40 (2014), 57-80. doi:10.1007/s11118-013-9341-1 Journal, arXiv
S.J. Gardiner and T. Sjödin, Stationary boundary points for a Laplacian growth problem in higher dimensions, Arch. Ration. Mech. Anal. 213 (2014), 503-526. doi:10.1007/s00205-014-0750-0 Journal

2013
T. Adamowicz, A. Björn, J. Björn and N. Shanmugalingam, Prime ends for domains in metric spaces, Adv. Math. 238 (2013), 459-505. doi:10.1016/j.aim.2013.01.014 Journal (Open access), arXiv
L. Malý, Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices, Ann. Acad. Sci. Fenn. Math. 38 (2013), 727-745. doi:10.5186/aasfm.2013.3831 pdf, Journal (Open access), arXiv
H. Shahgholian and T. Sjödin, Harmonic balls and the two-phase Schwarz function, Complex Var. Elliptic Equ. 58 (2013), 837-852. doi:10.1080/17476933.2011.622046 Journal, arXiv

2012
L. Malý, Calderón-type theorems for operators with non-standard endpoint behavior on Lorentz spaces, Math. Nachr. 285 (2012), 1450-1465. doi:10.1002/mana.201100095 Journal
S.J. Gardiner and T. Sjödin, Two-phase quadrature domains, J. Anal. Math. 116 (2012), 335-354. doi:10.1007/s11854-012-0009-3 Journal

2011
A. Björn and H. Riesel Table errata 2 to "Factors of generalized Fermat numbers", Math. Comp. 80 (2011), 1865-1866. doi:10.1090/S0025-5718-10-02371-9 Journal (Open access)
A. Björn and J. Björn, Power-type quasiminimizers, Ann. Acad. Sci. Fenn. Math. 36 (2011), 301-319. doi:10.5186/aasfm.2011.3619 pdf, Journal (Open access)
Z. Farnana, Pointwise regularity for solutions of double obstacle problems on metric spaces, Math. Scand. 109 (2011), 185-200. doi:10.7146/math.scand.a-15184 Journal (Open access)

2010
A. Björn, p-harmonic functions with boundary data having jump discontinuities and Baernstein's problem, J. Differential Equations 249 (2010), 1-36. doi:10.1016/j.jde.2010.03.002 Journal (Open access)
A. Björn, Cluster sets for Sobolev functions and quasiminimizers, J. Anal. Math. 112 (2010), 49-77. doi:10.1007/s11854-010-0025-0 Journal
A. Björn, J. Björn and N. Marola, BMO, integrability, Harnack and Caccioppoli inequalities for quasiminimizers, Ann. Inst. H. Poincaré C Anal. Non Linéaire 27 (2010), 1489-1505. doi:10.1016/j.anihpc.2010.09.005 Journal (Open access)
A. Björn, J. Björn and M. Parviainen, Lebesgue points and the fundamental convergence theorem for superharmonic functions on metric spaces, Rev. Mat. Iberoam. 26 (2010), 147-174. doi:10.4171/RMI/598 Journal (Open access)
J. Björn, Orlicz-Poincaré inequalities, maximal functions and A_Φ-conditions, Proc. Roy. Soc. Edinburgh Sect. A 140 (2010), 31-48. doi:10.1017/S0308210508000772 Journal
M. Eleuteri, Z. Farnana, O. E. Kansanen and R. Korte, Stability of solutions of the double obstacle problem on metric spaces, J. Anal. 18 (2010), 145-160. Journal
Z. Farnana, Continuous dependence on obstacles for the double obstacle problem on metric spaces, Nonlinear Anal. 73 (2010), 2819-2830. doi:10.1016/j.na.2010.06.023 Journal
Z. Farnana, Convergence results for obstacle problems on metric spaces, J. Math. Anal. Appl. 371 (2010), 436-446. doi:10.1016/j.jmaa.2010.05.044 Journal (Open access)

2009
A. Björn, J. Björn, T. Mäkäläinen and M. Parviainen, Nonlinear balayage on metric spaces, Nonlinear Anal. 71 (2009), 2153-2171. doi:10.1016/j.na.2009.01.051 Journal, Parallel publication
A. Björn and O. Martio, Pasting lemmas and characterizations of boundary regularity for quasiminimizers, Results Math. 55 (2009), 265-279. doi:10.1007/s00025-009-0437-2 Journal
J. Björn, Necessity of a Wiener type condition for boundary regularity of quasiminimizers and nonlinear elliptic equations, Calc. Var. Partial Differential Equations 35 (2009), 481-496. doi:10.1007/s00526-008-0216-z Journal
Z. Farnana, The double obstacle problem on metric spaces, Ann. Acad. Sci. Fenn. Math. 34 (2009), 261-277. Journal (Open access)

2008
A. Björn, A regularity classification of boundary points for p-harmonic functions and quasiminimizers, J. Math. Anal. Appl. 338 (2008), 39-47. doi:10.1016/j.jmaa.2007.04.068 Journal (Open access), Parallel publication
A. Björn, J. Björn and N. Shanmugalingam, Quasicontinuity of Newton-Sobolev functions and density of Lipschitz functions on metric spaces, Houston J. Math. 34 (2008), 1197-1211. Journal
J. Björn, Fine continuity on metric spaces, Manuscripta Math. 125 (2008), 369-381. doi:10.1007/s00229-007-0154-7 Journal
S. J. Gardiner and T. Sjödin, Convexity and the exterior inverse problem of potential theory, Proc. Amer. Math. Soc. 136 (2008), 1699-1703. doi:10.1090/S0002-9939-07-09228-3 Journal (Open access)

2007
A. Björn, Weak barriers in nonlinear potential theory, Potential Anal. 27 (2007), 381-387. doi:10.1007/s11118-007-9064-2 Journal, Parallel publication
A. Björn and J. Björn, Approximations by regular sets and Wiener solutions in metric spaces, Comment. Math. Univ. Carolin. 48 (2007), 343-355. pdf, Journal (Open access)
A. Björn, J. Björn and N. Shanmugalingam Sobolev extensions of Hölder continuous and characteristic functions on metric spaces, Canadian J. Math. 59 (2007), 1135-1153. doi:10.4153/CJM-2007-049-7 Journal (Open access)
J. Björn and N. Shanmugalingam, Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces, J. Math. Anal. Appl. 332 (2007), 190-208. doi:10.1016/j.jmaa.2006.09.064 Journal (Open access)
S. J. Gardiner and T. Sjödin, Quadrature domains for harmonic functions, Bull. Lond. Math. Soc. 39 (2007), 586-590. doi:10.1112/blms/bdm047 Journal
T. Sjödin, On the structure of partial balayage, Nonlinear Anal. 67 (2007), 94-102. doi:10.1016/j.na.2006.05.001 Journal
T. Sjödin, Approximation in the cone of positive harmonic functions, Potential Anal. 27 (2007), 271-280. doi:10.1007/s11118-007-9059-z Journal

2006
A. Björn, Removable singularities for bounded p-harmonic and quasi(super)harmonic functions, Ann. Acad. Sci. Fenn. Math. 31 (2006), 71-95. Journal (Open access)
A. Björn, Removable singularities in weighted Bergman spaces, Czechoslovak Math. J. 56 (2006), 179-227. doi:10.1007/s10587-006-0012-x Journal, Parallel publication
A. Björn, A weak Kellogg property for quasiminimizers, Comment. Math. Helv. 81 (2006), 809-825. doi:10.4171/CMH/75 Journal (Open access)
A. Björn and J. Björn, Boundary regularity for p-harmonic functions and solutions of the obstacle problem on metric spaces, J. Math. Soc. Japan 58 (2006), 1211-1232. Journal (Open access)
A. Björn, J. Björn and N. Shanmugalingam, A problem of Baernstein on the equality of the p-harmonic measure of a set and its closure, Proc. Amer. Math. Soc. 134 (2006), 509-519. doi:10.1090/S0002-9939-05-08187-6 Journal (Open access), Parallel publication
A. Björn and N. Marola, Moser iteration for (quasi)minimizers on metric spaces, Manuscripta Math. 121 (2006), 339-366. doi:10.1007/s00229-006-0040-8 Journal, Parallel publication
J. Björn, S. Buckley and S. Keith, Admissible measures in one dimension, Proc. Amer. Math. Soc. 134 (2006), 703-705. doi:10.1090/S0002-9939-05-07925-6 Journal (Open access)
T. Sjödin, Mother bodies of algebraic domains in the complex plane, Complex Var. Elliptic Equ. 51 (2006), 357-369. doi:10.1080/17476930600610049 Journal

2005
A. Björn, Characterizations of p-superharmonic functions on metric spaces, Studia Math. 169 (2005), 45-62. doi:10.4064/sm169-1-3 Journal (Open access)
A. Björn and H. Riesel, Table errata on "Factors of generalized Fermat numbers", Math. Comp. 74 (2005), 2099. doi:10.1090/S0025-5718-05-01816-8 Journal (Open access)
J. Björn and J. Onninen, Orlicz capacities and Hausdorff measures on metric spaces, Math. Z. 251 (2005), 131-146. doi:10.1007/s00209-005-0792-y Journal

2003
A. Björn, Removable singularities for analytic functions in BMO and locally Lipschitz spaces, Math. Z. 244 (2003), 805-835. doi:10.1007/s00209-003-0524-0 Journal, Parallel publication
A. Björn, J. Björn and N. Shanmugalingam, The Dirichlet problem for p-harmonic functions on metric spaces, J. Reine Angew. Math. 556 (2003), 173-203. doi:10.1515/crll.2003.020 Journal
A. Björn, J. Björn and N. Shanmugalingam, The Perron method for p-harmonic functions in metric spaces, J. Differential Equations 195 (2003), 398-429. doi:10.1016/S0022-0396(03)00188-8 Journal (Open access), Parallel publication

2002
N. Arcozzi and A. Björn, Dominating sets for analytic and harmonic functions and completeness of weighted Bergman spaces, Math. Proc. Roy. Irish Acad. 102A (2002), 175-192. doi:10.3318/PRIA.2002.102.2.175 Journal
A. Björn, Properties of removable singularities for Hardy spaces of analytic functions, J. Lond. Math. Soc. 66 (2002), 651-670. doi:10.1112/S002461070200354X Journal
J. Björn, Boundary continuity for quasiminimizers on metric spaces, Illinois J. Math. 46 (2002), 383-403. doi:10.1215/ijm/1258136199 Journal (Open access)
J. Björn, Mappings with dilatation in Orlicz spaces, Collect. Math. 53 (2002), 303-311. Journal (Open access)

2001
A. Björn, Removable singularities for H ^p spaces of analytic functions, 0<p<1, Ann. Acad. Sci. Fenn. Math. 26 (2001), 155-174. Journal (Open access)
J. Björn, Boundedness and differentiability for nonlinear elliptic systems, Trans. Amer. Math. Soc. 353 (2001), 4545-4565. doi:10.1090/S0002-9947-01-02834-3 Journal (Open access)
J. Björn, Poincar'e inequalities for powers and products of admissible weights, Ann. Acad. Sci. Fenn. Math. 26 (2001), 175-188. Journal (Open access)
J. Björn, P. MacManus and N. Shanmugalingam, Fat sets and pointwise boundary estimates for p-harmonic functions in metric spaces, J. Anal. Math. 85 (2001), 339-369. doi:10.1007/BF02788087 Journal

2000
J. Björn, L^q-differentials for weighted Sobolev spaces, Michigan Math. J. 47 (2000), 151-161. doi:10.1307/mmj/1030374674 Journal (Open access)
J. Björn and V. Maz'ya, Capacitary estimates for solutions of the Dirichlet problem for second order elliptic equations in divergence form, Potential Anal. 12 (2000), 81-113. doi:10.1023/A:1008670611142 Journal

1998
A. Björn Removable singularities for Hardy spaces, Complex Variables Theory Appl. 35 (1998), 1-25. doi:10.1080/17476939808815069 Journal, Parallel publication
A. Björn, Removable singularities on rectifiable curves for Hardy spaces of analytic functions. Math. Scand. 83 (1998), 87-102. doi:10.7146/math.scand.a-13844 Journal (Open access)
A. Björn and Riesel, H., Factors of generalized Fermat numbers, Math. Comp. 67 (1998), 441-446 + 49 pp. of tables on micro-fiche. doi:10.1090/S0025-5718-98-00891-6 Journal (Open access) (Table erratas see 2005 and 2011 above.)

1997
J. Björn, Regularity at infinity for a mixed problem for degenerate elliptic operators in a half-cylinder, Math. Scand. 81 (1997), 101-126. pdf, Journal (Open access)

1994
J. Ježková [Björn], Boundedness and pointwise differentiability of weak solutions to quasi-linear elliptic differential equations and variational inequalities, Comment. Math. Univ. Carolin. 35 (1994), 63-80. pdf, Journal (Open access)

Refereed conference proceedings

2014
S. J. Gardiner and T. Sjödin, Quadrature domains and their two-phase counterparts, in Harmonic and Complex Analysis and its Applications, pp. 261-285, Trends Math., Birkhäuser, Cham, 2014. doi:10.1007/978-3-319-01806-5_5 Publication

2009
A. Björn and J. Björn, First-order Sobolev spaces on metric spaces, in Function Spaces, Inequalities and Interpolation (Paseky, 2009), pp. 1-29, Matfyzpress, Prague, 2009.
S. J. Gardiner and T. Sjödin, Partial balayage and the exterior inverse problem of potential theory, in Potential theory and stochastics in Albac, Theta Ser. Adv. Math. 11, pp. 111-123, Theta, Bucharest, 2009.
S. J. Gardiner and T. Sjödin, Potential theory in Denjoy domains, in Analysis and mathematical physics, pp. 143-166, Trends Math., Birkhäuser, Basel, 2009. doi:10.1007/978-3-7643-9906-1_8 Publication

2006
J. Björn, Wiener criterion for Cheeger p-harmonic functions on metric spaces, in Potential Theory in Matsue, Advanced Studies in Pure Mathematics 44, pp. 103-115, Mathematical Society of Japan, Tokyo, 2006. pdf, Publication (Open access)

2005
T. Sjödin, Quadrature identities and deformation of quadrature domains, in Quadrature Domains and their Applications, Operator Theory, Advances and Applications 156, pp. 239-255, Birkhäuser, Basel, 2005. doi:10.1007/3-7643-7316-4_12 Publication

2003
A. Björn, p-harmonic measures and the Perron method for p-harmonic functions}, in Future Trends in Geometric Function Theory RNC Workshop Jyväskylä 2003, Rep. Univ. Jyväskylä Dep. Math. Stat. 92, pp. 23-29, Univ. Jyväskylä, Jyväskylä, 2003.
A. Björn, Removable singularities for analytic functions in Hardy spaces, BMO and locally Lipschitz spaces, in Progress in Analysis. Proceedings of the 3rd International ISAAC Congress (Berlin, 2001), vol. 1, pp. 445-450, World Scientific, Singapore, 2003. doi:10.1142/9789812794253_0050 Publication
J. Björn, Dirichlet problem for p-harmonic functions in metric spaces, in Future Trends in Geometric Function Theory RNC Workshop Jyväskylä 2003, Rep. Univ. Jyväskylä Dep. Math. Stat. 92, pp. 31-38, Univ. Jyväskylä, Jyväskylä, 2003.

1996
A. Björn, Removable singularities for Hardy spaces in subdomains of C, in Potential Theory - ICPT 94 (J. Král, J. Lukes, I. Netuka and J. and Veselý, eds.), pp. 287-295, de Gruyter, Berlin-New York, 1996. doi:10.1515/9783110818574.287 Publication
A. Björn, Some open problems relating removable singularities for Hardy spaces and Hausdorff measures, in Potential Theory - ICPT 94 (J. Král, J. Lukes, I. Netuka and J. and Veselý, eds.), p. 474, de Gruyter, Berlin-New York, 1996. doi:10.1515/9783110818574.473 Publication

1993
H. Riesel and A. Björn, Generalized Fermat numbers, in Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics (W.Gautschi, ed.), Proc. Symp. Appl. Math. 48, pp. 583-587, Amer. Math. Soc., Providence, RI, 1994. doi:10.1090/psapm/048/1314895 Publication

Popular science articles

2016
A. Björn, HbA_1c according to different standards, 2016. Publication (Open access)
A. Björn, HbA_1c enligt olika standarder, 2016 (in Swedish). Publication (Open access)
A. Björn, HbA_1c podle různých standardů, 2016 (in Czech). Publication (Open access)

2004
A. Björn, Why is there no Nobel prize in mathematics?, De Morgan Association Newsletter, Issue 11, Dept. of Maths., University College London, London, 2003/04.

Master's theses

David Manolis, Continuous primitives with infinite derivatives, 2023 (supervisor A. Björn, examiner J. Björn).
Andreas Christensen, Capacity estimates and Poincaré inequalities for the weighted bow-tie, 2017 (supervisor A. Björn, examiner J. Björn).
Hanna Svensson [Ström], Radiella vikter i Rⁿ och lokala dimensioner, 2014 (supervisor J. Björn, examiner A. Björn).
Hannes Uppman, The Reflection Principle for One-dimensional Quasiminimizers, 2009 (supervisor A. Björn).
Karl Tomas Andersson [Lööw], An iterative solution method for p-harmonic functions on finite graphs with an implementation, 2009 (supervisor A. Björn). Thesis, Program
John Karlsson, Lebesgue points, Hölder continuity and Sobolev functions, 2008 (supervisor J. Björn).
Patrik Leifson, Fractal sets and dimensions, 2006 (supervisor J. Björn).
David Färm, Upper gradients and Sobolev spaces on metric spaces, 2006 (supervisor J. Björn).
Lisa Hallingström, Primkontroll av tal på formen k · 2^q+1 med program i Fortran 77, 2003 (supervisor A. Björn).
Svante Landgraf, Dominating sets for real parts of holomorphic functions, 2003 (supervisor A. Björn).
Joakim Gustafsson, An implementation and optimization of an algorithm for reducing formulae in second-order logic, 1996 (supervisor P. Doherty, examiner A. Björn).
Anders Björn, The number of integers less that x, being products of primes of the form q=2rl+a only, 1988 (supervisor H. Riesel).

Bachelor's theses

Simon Bladh, Admissibility and A^p classes for radial weights in Rⁿ, 2023 (supervisor J. Björn, examiner A. Björn).
Ludvig Fagrell, Hyperbolic fillings of bounded metric spaces, 2023 (supervisor A. Björn, examiner J. Björn).
Måns Alskog, The history of the Dirichlet Problem for Laplace’s equation, 2023 (supervisor A. Björn, examiner J. Björn).
Samuel Erickson Andersson and David Wiman, An introduction to metric spaces, 2022 (supervisor A. Björn, examiner J. Björn).
Jakob Jonsson, Exponent sets and Muckenhoupt A_p-weights, 2022 (supervisor J. Björn, examiner A. Björn).
David Manolis, The Henstock–Kurzweil integral, 2020 (supervisor A. Björn, examiner J. Björn).
Maria Miranda Navarro, Comparative study of several bases in functional analysis, 2018 (supervisor J. Björn).
Erik Jönsson, Tug-of-war games of the p-Laplacian for analysts, 2018 (supervisor J. Björn, examiner A. Björn).
Erik Sätterqvist, Sequences of functions: Different notions of convergence and how they are reelated, 2018 (supervisor J. Björn, examiner A. Björn).
Sofia Svensson, Lokala dimensioner och radiella vikter i Rⁿ, 2017 (supervisor J. Björn, examiner A. Björn).
Karl Nygren, Trust logics and their horn fragments: formalizing socio-cognitive aspects of trust, 2015 (superviser Andrzej Szałas, examiner A. Björn).
Hannah Schäfer Sjöberg, A problem in number theory, 2013 (supervisor A. Björn).
Adam Schill Collberg, The last two digits of m^k, 2012 (supervisor Gao Peng, examiner A. Björn).
Jimmie Enhäll, Ett problem inom talteori, 2005 (supervisor A. Björn).
Tobias Svensson, Common factors in generalized Fermat numbers, 2005 (supervisor A. Björn).