On semilinear equations with free boundary conditions on stratified Lie groups

TL;DR

This paper proves the existence of solutions to semilinear equations with free boundary conditions on stratified Lie groups, introducing a key monotonicity condition that aids in establishing solution regularity.

Contribution

It presents the first existence proof for such equations on stratified Lie groups and introduces a crucial monotonicity condition for regularity analysis.

Findings

Existence of solutions established for semilinear equations with free boundaries on stratified Lie groups.

A monotonicity condition is proved, essential for regularity of solutions.

The approach advances understanding of PDEs on non-Euclidean structures.

Abstract

In this paper we establish existence of a solution to a semilinear equation with free boundary conditions on stratified Lie groups. In the process, a monotonicity condition is proved, which is quintessential in establishing the regularity of the solution.