Jarkko Siltakoski
Published 2017-10-21Version 1
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.
On equivalence of entropy and viscosity solutions to degenerate parabolic equations and applications
A New Proof of the Equivalence of Weak and Viscosity Solutions to the Homogeneous $\texttt{p}(\cdot)$-Laplacian in $\mathbb{R}^n$
To the theory of viscosity solutions for uniformly elliptic Isaacs equations
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