Analysis of a free boundary problem on stratified Lie group

TL;DR

This paper develops a variational approach to analyze elliptic free boundary problems on stratified Lie groups, establishing existence results via monotonicity and mountain pass techniques in a non-Euclidean setting.

Contribution

It introduces a novel variational framework for free boundary problems on stratified Lie groups, leveraging non-Euclidean monotonicity and approximation methods.

Findings

Proved existence of solutions using mountain pass points.

Established a monotonicity result in a non-Euclidean context.

Showed solutions are limits of approximating C1-functionals.

Abstract

We present a variational framework for studying the existence of solutions of a class of elliptic free boundary problems on stratified Lie groups. Using the important monotonicity result in a Non-Euclidean setup, we prove that our solution is the limit of mountain pass points of a sequence of C1-functionals approximating the energy