Regularity of p(·)-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.

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.

DOI : 10.1016/j.anihpc.2013.07.012
Classification : 35J67, 31C45, 46E35
Mots clés : 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
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     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},
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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. http://www.numdam.org/articles/10.1016/j.anihpc.2013.07.012/

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