Existence, comparison principle and uniqueness for fully nonlinear anisotropic evolution equations

TL;DR

This paper establishes existence, comparison principle, and uniqueness for solutions to a class of fully nonlinear anisotropic evolution equations under specific conditions.

Contribution

It introduces new existence and uniqueness results for anisotropic evolution equations with a gradient condition on solutions.

Findings

Existence of solutions to the Cauchy-Dirichlet problem for the class of equations.

Comparison principle proved for these equations.

Uniqueness of solutions established under certain exponent conditions.

Abstract

We prove the existence of solutions to the Cauchy-Dirichlet problem associated with a class of fully nonlinear anisotropic evolution equations. We prove a comparison principle and conclude the uniqueness of solutions. All results are obtained under a closeness assumption on the exponents which guarantees that a certain power of the solution has a gradient.