Nonlinear elliptic inclusions with unilateral constraint and dependence on the gradient

TL;DR

This paper proves the existence of smooth solutions for a nonlinear Neumann elliptic inclusion involving unilateral constraints and gradient dependence, using topological methods and Moreau-Yosida approximations.

Contribution

It introduces a novel approach combining topological methods and Moreau-Yosida approximations to handle gradient-dependent nonlinear elliptic inclusions with unilateral constraints.

Findings

Existence of smooth solutions established.

Framework accommodates problems with unilateral constraints.

Method applicable to gradient-dependent nonlinear elliptic problems.

Abstract

We consider a nonlinear Neumann elliptic inclusion with a source (reaction term) consisting of a convex subdifferential plus a multivalued term depending on the gradient. The convex subdifferential incorporates in our framework problems with unilateral constraints (variational inequalities). Using topological methods and the Moreau-Yosida approximations of the subdifferential term, we establish the existence of a smooth solution.