Ickelinjär potentialteori

Vid tavlan: Nageswari Shanmugalingam, Anders Björn, Jana Björn och Tomas Sjödin
Nageswari Shanmugalingam, Anders Björn, Jana Björn och Tomas Sjödin.

Vår forskargrupp är främst intresserad av analys på metriska rum, speciellt ickelinjär potentialteori associerade med p-harmoniska funktioner och kvasiminimerare i euklidiska och metriska rum. Vi är också intresserade av första ordningens sobolevrum, speciellt så kallade newtonrum på metriska rum.

En populärvetenskaplig beskrivning av vår forskning

Differentialekvationer och analys på metriska rum

Konferenser

Vi har arrangerat följande konferenser i Linköping:

Geometric Analysis on Metric Spaces, 22-24 maj 2017 
PDEs, Potential Theory and Function Spaces, 14-18 juni 2015 
Nonlinear problems for Δp and Δ, 10-14 augusti 2009

Gruppmedlemmar

Tidigare gruppmedlemmar

Samarbete

Personer som vi samarbetar eller har nära kontakter med.

Hiroaki Aikawa vid Hokkaido University, Sapporo 
Stephen Gardiner vid University College Dublin 
Ugo Gianazza vid University of Pavia 
Agnieszka Kałamajska vid Warsaw University 
Juha Kinnunen och Riikka Korte vid Aalto-universitetet, Helsingfors 
Visa Latvala vid University of Eastern Finland, Joensuu 
Juha Lehrbäck och Mikko Parviainen vid Jyväskylä University 
Xining Li vid Sun Yat-sen University, Guangzhou (Kanton) 
Jan Malý vid Charles University, Prag 
Olli Martio och Xiao Zhong vid Helsingfors universitet
Juhana Siljander vid University of Chicago

Publikationer

Listan nedanför innehåller gruppmedlemmarnas matematiska publikationerna (i omvänd kronologisk ordning).

Böcker

A. Björn and J. BjörnNonlinear 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 AMSCorrections and clarifications (last updated 3 May 2018). 
The authors' profit from this book is donated to Barndiabetesfonden (The Swedish Child Diabetes Fund). 
A. Asratian, A. Björn and B. O. TuressonDiskret Matematik, 15th ed., Matematiska institutionen, Linköpings universitet, 2015, 285 pp. (Swedish).

Doktorsavhandlingar

L. MalýSobolev-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. FarnanaThe 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. SjödinTopics 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. BjörnInterior 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. BjörnRemovable 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).

Licentiatavhandlingar

L. MalýNewtonian 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. FarnanaThe 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).

Master- och kandidatuppsatser, se längst ner.

Preprints

A. Björn and J. Björn, A uniqueness result for functions with zero fine gradient on quasiconnected sets, Preprint, 2018. arXiv
A. Björn, J. Björn and M. Parviainen, The tusk condition and Petrovskii criterion for the normalized p-parabolic equation, Preprint, 2017. arXiv
A. Björn, J. Björn and N. Shanmugalingam, Locally p-admissible measures on R, Preprint, 2018. arXiv
A. Björn, J. Björn and N. Shanmugalingam, The Liouville theorem for p-harmonic functions and quasiminimizers with finite energy Preprint, 2018. arXiv
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, Preprint, 2017. arXiv, Preprint CVGMT
L. Malý, Trace and extension theorems for Sobolev-type functions in metric spaces, Preprint, 2017. arXiv

Granskade artiklar

To appear
H. Aikawa, A. Björn, J. Björn and N. Shanmugalingam, Dichotomy of global capacity density in metric measure spaces, to appear in Adv. Calc. Var. doi:10.1515/acv-2016-0066 Journal, arXiv, Preprint CVGMT
A. Björn, The Kellogg property and boundary regularity for p-harmonic functions with respect to the Mazurkiewicz boundary and other compactifications, to appear in Complex Var. Elliptic Equ. doi:10.1080/17476933.2017.1410799 Journal, arXiv
A. Björn and J. Björn, Local and semilocal Poincaré inequalities on metric spaces, to appear in J. Math. Pures Appl. doi:10.1016/j.matpur.2018.05.005 Journal, arXiv
A. Björn and J. Björn, Poincaré inequalities and Newtonian Sobolev functions on noncomplete metric spaces, to appear in J. Differential Equations. doi:10.1016/j.jde.2018.07.029 Journal, arXiv
A. Björn and J. Björn, Tensor products and sums of p-harmonic functions, quasiminimizers and p-admissible weights, to appear in Proc. Amer. Math. Soc. doi:10.1090/proc/14170 Journal, arXiv
S. J. Gardiner, M. Ghergu and T. Sjödin, Isoperimetric inequalities for Bergman analytic content, to appear in Indiana Univ. Math. J. Preprint
S. J. Gardiner and T. Sjödin, On a conjecture of Král concerning the subharmonic extension of continuously differentiable functions, to appear in Math. Bohem.

2018
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, 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, 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, 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, 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. Journal, 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 JournalarXiv 
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-2014-0099JournalarXiv 
A. Björn, J. Björn and R. Korte, Minima of quasisuperminimizers, Nonlinear Anal. 155 (2017), 264-284. doi:10.1016/j.na.2017.02.003 JournalarXiv 
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/s00209-016-1797-4Journal (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-yJournalarXiv 
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-zJournal (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 JournalarXiv 
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 pdfJournalarXiv 
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 JournalPreprint 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,arXiv
L. Malý, Newtonian spaces based on quasi-Banach function lattices, Math. Scand. 119 (2016), 133-160. doi:10.7146/math.scand.a-24188 JournalarXiv 
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,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 JournalarXiv

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 JournalPreprint 
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 JournalPreprint 
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 JournalarXiv 
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,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 JournalPreprint 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 JournalPreprint 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 JournalarXiv 
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 pdfJournalarXiv

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 JournalPreprint 
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 JournalarXiv 
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 JournalarXiv 
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.2013.01.014JournalarXiv 
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 pdfJournalarXiv 
H. Shahgholian and T. Sjödin, Harmonic balls and the two-phase Schwarz function, Complex Var. Elliptic Equ. 58 (2013), 837-852. doi:10.1080/17476933.2011.622046JournalarXiv

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.201100095Journal 
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 
A. Björn and J. Björn, Power-type quasiminimizers, Ann. Acad. Sci. Fenn. Math. 36 (2011), 301-319. doi:10.5186/aasfm.2011.3619 pdfJournal 
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

2010 
A. Björnp-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 
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 Anal. Non Linéaire 27 (2010), 1489-1505. doi:10.1016/j.anihpc.2010.09.005 Journal 
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 
J. Björn, Orlicz-Poincaré inequalities, maximal functions and AΦ-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.2010.06.023Journal 
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

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/s00025-009-0437-2Journal 
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

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.2007.04.068JournalParallel 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

2007 
A. Björn, Weak barriers in nonlinear potential theory, Potential Anal. 27 (2007), 381-387. doi:10.1007/s11118-007-9064-2 JournalParallel publication 
A. Björn and J. Björn, Approximations by regular sets and Wiener solutions in metric spaces, Comment. Math. Univ. Carolin. 48 (2007), 343-355. pdfJournal 
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 
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 
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 
A. Björn, Removable singularities in weighted Bergman spaces, Czechoslovak Math. J. 56 (2006), 179-227. doi:10.1007/s10587-006-0012-x JournalParallel publication 
A. Björn, A weak Kellogg property for quasiminimizers, Comment. Math. Helv. 81 (2006), 809-825. doi:10.4171/CMH/75 Journal 
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
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 JournalParallel 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 JournalParallel 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 
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 
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 
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 JournalParallel 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, J. Differential Equations 195 (2003), 398-429. doi:10.1016/S0022-0396(03)00188-8 JournalParallel 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. Journal 
J. Björn, Mappings with dilatation in Orlicz spaces, Collect. Math. 53 (2002), 303-311.

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 
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 
J. Björn, Poincar\'e inequalities for powers and products of admissible weights, Ann. Acad. Sci. Fenn. Math. 26 (2001), 175-188. Journal 
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. BjörnLq-differentials for weighted Sobolev spaces, Michigan Math. J. 47 (2000), 151-161. doi:10.1307/mmj/1030374674 Journal 
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 JournalParallel 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 
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/S0025-5718-98-00891-6Journal

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

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. pdfJournal

Granskade konferensproceedings

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. pdfPublication

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. Björnp-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

Populärvetenskapliga artiklar

2016 
A. Björn, HbA1c according to different standards, 2016. Publication 
A. Björn, HbA1c enligt olika standarder, 2016 (in Swedish). Publication 
A. Björn, HbA1c podle různých standardů, 2016 (in Czech). Publication

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.

Masteruppsatser

Andreas ChristensenCapacity 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 UppmanThe 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). ThesisProgram 
John KarlssonLebesgue points, Hölder continuity and Sobolev functions, 2008 (supervisor J. Björn). 
Patrik LeifsonFractal sets and dimensions, 2006 (supervisor J. Björn). 
David FärmUpper gradients and Sobolev spaces on metric spaces, 2006 (supervisor J. Björn). 
Lisa Hallingström, Primkontroll av tal på formen k · 2q+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).

Kandidatuppsatser

Erik JönssonTug-of-war games of the p-Laplacian for analysts, 2018 (supervisor J. Björn, examiner A. Björn). 
Erik SätterqvistSequences of functions: Different notions of convergence and how they are reelated, 2018 (supervisor J. Björn, examiner A. Björn). 
Sofia SvenssonLokala dimensioner och radiella vikter i Rn, 2017 (supervisor J. Björn, examiner A. Björn). 
Karl NygrenTrust logics and their horn fragments: formalizing socio-cognitive aspects of trust, 2015 (superviser Andrzej Szałas, examiner A. Björn). 
Hannah Schäfer SjöbergA problem in number theory, 2013 (supervisor A. Björn). 
Adam Schill CollbergThe last two digits of mk, 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).

En populärvetenskaplig beskrivning av vår forskning