A Stability Result for the $\infty$-Laplace Equation

TL;DR

This paper studies a degenerate elliptic PDE related to the infinity Laplace equation, establishing a stability result and analyzing the Gamma-convergence of associated functionals.

Contribution

It provides a new stability theorem for solutions of the infinity Laplace equation and explores the Gamma-convergence of related functionals.

Findings

Established a stability result for the $ abla$-Laplace equation

Analyzed the Gamma-convergence of the associated functionals

Contributed to understanding the variational structure of the $ abla$-Laplace equation

Abstract

We investigate a degenerate elliptic PDE related to the $\infty$-Laplace equation $\Delta_{\infty}u=0$. A stability result is derived. The $\Gamma$-convergence of the corresponding functionals is investigated.