Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points
2014 (English)In: Annales de l'Institut Henri Poincare. Analyse non linéar, ISSN 0294-1449, Vol. 31, no 6, 1131-1153 p.Article in journal (Refereed) Published
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.
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
IdentifiersURN: urn:nbn:se:liu:diva-113374DOI: 10.1016/j.anihpc.2013.07.012ISI: 000346550400003OAI: oai:DiVA.org:liu-113374DiVA: diva2:781556
Funding Agencies|Swedish Research Council2015-01-162015-01-162016-05-04