Regularity of -superharmonic functions, the Kellogg property and semiregular boundary points
Tomasz Adamowicz
Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden, Institute of Mathematics, Polish Academy of Sciences, 00-956 Warsaw, PolandAnders Björn
Department of Mathematics, Linköping University, SE-581 83 Linköping, SwedenJana Björn
Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden
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Abstract
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.
Cite this article
Tomasz Adamowicz, Anders Björn, Jana Björn, Regularity of -superharmonic functions, the Kellogg property and semiregular boundary points. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 6, pp. 1131–1153
DOI 10.1016/J.ANIHPC.2013.07.012