Regularity for quasilinear vectorial elliptic systems through an iterative scheme with numerical applications

TL;DR

This paper introduces an iterative scheme for solving quasilinear elliptic systems with p-growth, extending previous quadratic case methods, and demonstrates its numerical applications and higher regularity results.

Contribution

It generalizes Koshelev's iterative approach from quadratic to p-growth systems and explores their regularity and numerical applications.

Findings

Successful implementation of the iterative scheme for p-growth systems.

Demonstrated higher regularity properties of solutions.

Provided numerical examples illustrating the method's effectiveness.

Abstract

We consider an iterative procedure to solve quasilinear elliptic systems with $p$-growth. The scheme was first considered by Koshelev in the quadratic case $p=2$. We present numerical applications as well as applications to higher regularity properties.