On existence of viscosity solutions for evolution $p(x)$-Laplace equation with one spatial variable

Ar. S. Tersenov

Sibirskij žurnal industrialʹnoj matematiki, Tome 27 (2024) no. 4, pp. 130-151

Résumé

In this paper, we study the first boundary value problem for $p(x)$-Laplacian with one spatial variable in the presence of gradient terms that do not satisfy the Bernstein—Nagumo condition. A class of gradient nonlinearities is defined, for which the existence of a viscosity solution that is Lipschitz continuous in $x$ and Hölder continuous in $t$ is proven.

Détail

Mots-clés : $p(x)$-Laplace equation
Keywords: Bernstein—Nagumo type condition, viscosity solutions, a priori estimates.

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