Bernoulli free boundary problem for the infinity Laplacian

TL;DR

This paper investigates the Bernoulli free boundary problem for the infinity Laplacian, establishing key properties like existence, uniqueness, regularity, and connections to p-Laplacian solutions.

Contribution

It provides the first comprehensive analysis of the Bernoulli free boundary problem specifically for the infinity Laplacian, including solution characterization and regularity results.

Findings

Existence and uniqueness of solutions above a certain threshold.

Regularity properties of the solutions.

Relationship with solutions to the p-Laplacian Bernoulli problem.

Abstract

We study the interior Bernoulli free boundary problem for the infinity Laplacian. Our results cover existence, uniqueness, and characterization of solutions (above a threshold representing the "infinity Bernoulli constant"), their regularity, and their relationship with the solutions to the interior Bernoulli problem for the $p$-laplacian.