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The Dirichlet problem for -harmonic functions on the topologists comb
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9677-8321
2015 (English)In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 279, no 1-2, 389-405 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we study the Perron method for solving the -harmonic Dirichlet problem on the topologists comb. For functions which are bounded and continuous at the accessible points, we obtain invariance of the Perron solutions under arbitrary perturbations on the set of inaccessible points. We also obtain some results allowing for jumps and perturbations at a countable set of points.

Place, publisher, year, edition, pages
Springer Verlag (Germany) , 2015. Vol. 279, no 1-2, 389-405 p.
Keyword [en]
Boundary regularity; Dirichlet problem; Perron method; p-Harmonic function; Prime end boundary; Topologists comb
National Category
URN: urn:nbn:se:liu:diva-114418DOI: 10.1007/s00209-014-1373-8ISI: 000347831200019OAI: diva2:791980

Funding Agencies|Swedish Research Council; Swedish Fulbright Commission

Available from: 2015-03-02 Created: 2015-02-20 Last updated: 2015-03-02

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Björn, Anders
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Mathematics and Applied MathematicsThe Institute of Technology
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