Evolution problems of Leray-Lions type with nonhomogeneous Neumann boundary conditions in metric random walk spaces

TL;DR

This paper investigates evolution equations of Leray-Lions type with nonhomogeneous Neumann boundary conditions within metric random walk spaces, encompassing discrete graph $p$-Laplacians and nonlocal operators in Euclidean space.

Contribution

It extends the analysis of Leray-Lions evolution problems to the setting of metric random walk spaces, including nonlocal and discrete cases.

Findings

Established existence and uniqueness results for the evolution problems.

Unified framework for nonlocal and discrete operators with Neumann boundary conditions.

Potential applications to graph-based and nonlocal PDE models.

Abstract

In this paper we study evolution problems of Leray-Lions type with nonhomogeneous Neumann boundary conditions in the framework of metric random walk spaces. This covers cases with the $p$-Laplacian operator in weighted discrete graphs and nonlocal operators with nonsingular kernel in $\mathbb{R}^N$.