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

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

2011-01-02

arxiv.org/abs/1101.0418v1

Mathematics

Analysis of PDEs

Scientific paper

We establish that a closed set $E$ is removable for $C^{0,\alpha}$ H\"{o}lder
continuous $p(x)$-harmonic functions in a bounded open domain $\Omega$ of
$\mathbb{R}^n$, $n\geq 2$, provided that for each compact subset $K$ of $E$,
the $(n-p_K+\alpha(p_K-1))$-Hausdorff measure of $K$ is zero, where
$p_K=\max_{x\in K} p(x)$.

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