Existence and uniqueness for a quasilinear elliptic problem with nonlinear Robin conditions

TL;DR

This paper establishes the existence and uniqueness of weak solutions for a quasilinear elliptic PDE with nonlinear Robin boundary conditions on a domain with mixed boundary types, using monotone operator theory.

Contribution

It provides new existence and uniqueness results for a class of quasilinear elliptic problems with nonlinear Robin boundary conditions, expanding the theoretical understanding.

Findings

Proved existence of weak solutions under specified conditions.

Established uniqueness of solutions for the problem.

Applied monotone operator theory to handle nonlinear boundary conditions.

Abstract

This paper deals with an existence and uniqueness result of the weak solution for a quasilinear elliptic PDE with nonlinear Robin boundary conditions.This problem is defined on a domain whose boundary is the union of two disjoint surfaces.where a Dirichelet condition is prescribed on the exterior boundary and a nonlinear Robin condition on the interior one.To achieve that, we use the theory of monotone operators