Equivalence of viscosity and weak solutions for the normalized $p(x)$-Laplacian

Jarkko Siltakoski

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arXiv · 1710.07760

Equivalence of viscosity and weak solutions for the normalized $p(x)$-Laplacian

Jarkko Siltakoski

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Abstract

We show that viscosity solutions to the normalized $p(x)$-Laplace equation coincide with distributional weak solutions to the strong $p(x)$-Laplace equation when $p$ is Lipschitz and $\inf p>1$. This yields $C^{1,\alpha}$ regularity for the viscosity solutions of the normalized $p(x)$-Laplace equation. As an additional application, we prove a Rad\'o-type removability theorem.

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Jarkko Siltakoski. 2017-10-21. Equivalence of viscosity and weak solutions for the normalized $p(x)$-Laplacian. https://arxiv.org/abs/1710.07760

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