Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points

• 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

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

Publication and Content Type

ref (subject category)

art (subject category)