%0 Journal Article
%T Regularity of $p(\cdot)$-superharmonic functions, the Kellogg property and semiregular boundary points
%A Tomasz Adamowicz
%A Anders Bj£¿rn
%A Jana Bj£¿rn
%J Mathematics
%D 2013
%I arXiv
%R 10.1016/j.anihpc.2013.07.012
%X We study various boundary and inner regularity questions for $p(\cdot)$-(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for $p(\cdot)$-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 $p(\cdot)$-harmonic functions and give some new characterizations of $W^{1, p(\cdot)}_0$ spaces. We also show that $p(\cdot)$-superharmonic functions are lower semicontinuously regularized, and characterize them in terms of lower semicontinuously regularized supersolutions.
%U http://arxiv.org/abs/1302.0233v1