On the solvability of the Dirichlet problem for anisotropic parabolic equations in non-convex domains

Ar. S. Tersenov

Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 1, pp. 131-146.

Résumé

The Cauchy—Dirichlet problem in non-convex domains for anisotropic parabolic equation with time-dependent exponents and gradient term is considered. We state sufficient conditions that guarantee the existence and uniqueness of a viscosity solution which is Lipschitz continuous in the space variables and Hölder continuous in time.

Détail

Keywords: boundary value problems, a priori estimates, viscosity solutions. .
Mots-clés : anisotropic equations

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