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We study various boundary and inner regularity questions for -(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for -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 -harmonic functions and give some new characterizations of spaces. We also show that -superharmonic functions are lower semicontinuously regularized, and characterize them in terms of lower semicontinuously regularized supersolutions.
Keywords: Comparison principle, Kellogg property, lsc-regularized, Nonlinear potential theory, Nonstandard growth equation, Obstacle problem, $ p(\cdot )$-harmonic, Quasicontinuous, Regular boundary point, Removable singularity, Semiregular point, Sobolev space, Strongly irregular point, $ p(\cdot )$-superharmonic, $ p(\cdot )$-supersolution, Trichotomy, Variable exponent
@article{AIHPC_2014__31_6_1131_0,
author = {Adamowicz, Tomasz and Bj\"orn, Anders and Bj\"orn, Jana},
title = {Regularity of $ p(\cdot )$-superharmonic functions, the {Kellogg} property and semiregular boundary points},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {1131--1153},
publisher = {Elsevier},
volume = {31},
number = {6},
year = {2014},
doi = {10.1016/j.anihpc.2013.07.012},
mrnumber = {3280063},
zbl = {1304.35296},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2013.07.012/}
}
TY - JOUR AU - Adamowicz, Tomasz AU - Björn, Anders AU - Björn, Jana TI - Regularity of $ p(\cdot )$-superharmonic functions, the Kellogg property and semiregular boundary points JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 SP - 1131 EP - 1153 VL - 31 IS - 6 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2013.07.012/ DO - 10.1016/j.anihpc.2013.07.012 LA - en ID - AIHPC_2014__31_6_1131_0 ER -
%0 Journal Article %A Adamowicz, Tomasz %A Björn, Anders %A Björn, Jana %T Regularity of $ p(\cdot )$-superharmonic functions, the Kellogg property and semiregular boundary points %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 1131-1153 %V 31 %N 6 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2013.07.012/ %R 10.1016/j.anihpc.2013.07.012 %G en %F AIHPC_2014__31_6_1131_0
Adamowicz, Tomasz; Björn, Anders; Björn, Jana. Regularity of $ p(\cdot )$-superharmonic functions, the Kellogg property and semiregular boundary points. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 6, pp. 1131-1153. doi: 10.1016/j.anihpc.2013.07.012
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