# A free boundary optimization problem for the $\infty$-Laplacian

## TL;DR

This paper investigates a free boundary optimization problem involving the infinity-Laplacian in heat conduction, establishing existence, regularity, and geometric properties of solutions and free boundaries under certain constraints.

## Contribution

It introduces a novel free boundary problem governed by the infinity-Laplacian, providing new existence, regularity, and geometric insights into the solutions.

## Key findings

- Existence of solutions under given constraints
- Regularity results for the free boundary
- Geometric properties of the solution and free boundary

## Abstract

We study a free boundary optimization problem in heat conduction, ruled by the infinity-Laplace operator, with lower temperature bound and a volume constraint. We obtain existence and regularity results and derive geometric properties for the solution and the free boundaries.