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Regularity of p(.)-...
Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points
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- Adamowicz, Tomasz (author)
- Linköpings universitet,Matematik och tillämpad matematik,Tekniska högskolan
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- Björn, Anders (author)
- Linköpings universitet,Matematik och tillämpad matematik,Tekniska högskolan
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- Björn, Jana (author)
- Linköpings universitet,Matematik och tillämpad matematik,Tekniska högskolan
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(creator_code:org_t)
- Elsevier Masson / Institute Henri Poincar�, 2014
- 2014
- English.
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In: Annales de l'Institut Henri Poincare. Analyse non linéar. - : Elsevier Masson / Institute Henri Poincar�. - 0294-1449 .- 1873-1430. ; 31:6, s. 1131-1153
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Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- 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
Publication and Content Type
- ref (subject category)
- art (subject category)
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