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arXiv · 2111.06050

Hölder gradient regularity for the inhomogeneous normalized $p(x)$-Laplace equation

Jarkko Siltakoski
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Abstract

We prove the local gradient Hölder regularity of viscosity solutions to the inhomogeneous normalized $p(x)$-Laplace equation $$ -Δu-(p(x)-2)\frac{\left\langle D^{2}uDu,Du\right\rangle }{\left|Du\right|^{2}} = f(x), $$ where $p$ is Lipschitz continuous, $\inf p>1$, and $f$ is continuous and bounded.

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Jarkko Siltakoski. 2021-11-11. Hölder gradient regularity for the inhomogeneous normalized $p(x)$-Laplace equation. https://arxiv.org/abs/2111.06050

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