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Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.ORCID-id: 0000-0002-9677-8321
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.ORCID-id: 0000-0002-1238-6751
2014 (engelsk)Inngår i: Annales de l'Institut Henri Poincare. Analyse non linéar, ISSN 0294-1449, E-ISSN 1873-1430, Vol. 31, nr 6, s. 1131-1153Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
Elsevier Masson / Institute Henri Poincar� , 2014. Vol. 31, nr 6, s. 1131-1153
Emneord [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
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Identifikatorer
URN: urn:nbn:se:liu:diva-113374DOI: 10.1016/j.anihpc.2013.07.012ISI: 000346550400003OAI: oai:DiVA.org:liu-113374DiVA, id: diva2:781556
Merknad

Funding Agencies|Swedish Research Council

Tilgjengelig fra: 2015-01-16 Laget: 2015-01-16 Sist oppdatert: 2017-12-05

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Adamowicz, TomaszBjörn, AndersBjörn, Jana

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