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Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9677-8321
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-1238-6751
2014 (English)In: Annales de l'Institut Henri Poincare. Analyse non linéar, ISSN 0294-1449, E-ISSN 1873-1430, Vol. 31, no 6, 1131-1153 p.Article in journal (Refereed) Published
Abstract [en]

We study various boundary and inner regularity questions for p(.)-(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for p(.)-harmonic functions into three disjoint classes: regular, semiregular and strongly irregular points. Regular and especially semiregular points are characterized in many ways. The discussion is illustrated by examples. Along the way, we present a removability result for bounded p(.)-harmonic functions and give some new characterizations of W-0(1,p(.)) spaces. We also show that p(.)-superharmonic functions are lower semicontinuously regularized, and characterize them in terms of lower semicontinuously regularized supersolutions.

Place, publisher, year, edition, pages
Elsevier Masson / Institute Henri Poincar� , 2014. Vol. 31, no 6, 1131-1153 p.
Keyword [en]
Comparison principle; Kellogg property; Isc-regularized; Nonlinear potential theory; Nonstandard growth equation; Obstacle problem; p(.)-harmonic; Quasicontinuous; Regular boundary point; Removable singularity; Semiregular point; Sobolev space; Strongly irregular point; p(.)-superharmonic; p(.)-supersolution; Trichotomy; Variable exponent
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-113374DOI: 10.1016/j.anihpc.2013.07.012ISI: 000346550400003OAI: oai:DiVA.org:liu-113374DiVA: diva2:781556
Note

Funding Agencies|Swedish Research Council

Available from: 2015-01-16 Created: 2015-01-16 Last updated: 2017-12-05

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Adamowicz, TomaszBjörn, AndersBjörn, Jana

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