Dirichlet Problem for Coupled Elliptic Systems

TL;DR

This paper addresses the Dirichlet problem for coupled quasi-linear elliptic systems in regular bounded domains, providing a variational approach to establish existence and solutions.

Contribution

It introduces a variational method for solving the Dirichlet problem for a class of coupled quasi-linear elliptic systems in regular domains.

Findings

Established existence of solutions for the Dirichlet problem.

Developed a variational framework for coupled elliptic systems.

Extended previous results to more general systems.

Abstract

Let $\Omega $ be a bounded domain in $\mathbb{R}^{d}$ $\left( d\geq 2\right) $ pretty regular. We solve the variational Dirichlet problem for a class of quasi-linear elliptic systems.