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The Kellogg property and boundary regularity for p-harmonic functions with respect to the Mazurkiewicz boundary and other compactifications
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-9677-8321
2019 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 64, no 1, p. 40-63Article in journal (Refereed) Published
Abstract [en]

In this paper, boundary regularity for p-harmonic functions is studied with respect to the Mazurkiewicz boundary and other compactifications. In particular, the Kellogg property (which says that the set of irregular boundary points has capacity zero) is obtained for a large class of compactifications, but also two examples when it fails are given. This study is done for complete metric spaces equipped with doubling measures supporting a p-Poincare inequality, but the results are new also in unweighted Euclidean spaces.

Place, publisher, year, edition, pages
TAYLOR & FRANCIS LTD , 2019. Vol. 64, no 1, p. 40-63
Keywords [en]
Boundary regularity; capacity; Dirichlet problem; doubling measure; Kellogg property; metric space; p-harmonic function; Poincare inequality; regular point; resolutive-regular point; weak Kellogg property; Primary: 31C45; Secondary: 31E05; 35J66; 35J92; 49Q20
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-154702DOI: 10.1080/17476933.2017.1410799ISI: 000458164300004OAI: oai:DiVA.org:liu-154702DiVA, id: diva2:1292632
Note

Funding Agencies|Swedish Research Council [621-2007-6187, 621-2011-3139, 2016-03424]

Available from: 2019-02-28 Created: 2019-02-28 Last updated: 2019-02-28

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  • sv-SE
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