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

Along the way, we present a removability result for bounded p(⋅)-harmonic functions and give some new characterizations of W01,p(⋅) spaces. We also show that p(⋅)-superharmonic functions are lower semicontinuously regularized, and characterize them in terms of lower semicontinuously regularized supersolutions.