Removable Sets for Hölder Continuous p(x)-Harmonic Functions

2011/01/02 by A. Lyaghfouri, Lyaghfouri, A.
Mathematics · #35J60 #35J70 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35J60 #msc:35J70

paper · pdf · doi:10.48550/arxiv.1101.0418

arxiv created 2011/01/02 · arxiv updated 2011/01/04

Abstract

We establish that a closed set E is removable for C^0,α Hölder continuous p(x)-harmonic functions in a bounded open domain Ω of ℝⁿ, n≥ 2, provided that for each compact subset K of E, the (n-p_K+α(p_K-1))-Hausdorff measure of K is zero, where p_K=max_{x∈ K} p(x).

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