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

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 $\mathbb{R}^n$, $n\geq 2$, provided that for each compact subset $K$ of $E$, the $(n-p_K+α(p_K-1))$-Hausdorff measure of $K$ is zero, where $p_K=\max_{x\in K} p(x)$.

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