# Almost minimizers of the one-phase free boundary problem

## TL;DR

This paper studies almost minimizers in the one-phase free boundary problem, establishing their Lipschitz regularity and partial free boundary regularity using a novel viscosity solutions approach.

## Contribution

It introduces a new method based on non-infinitesimal viscosity solutions to prove regularity results for almost minimizers, differing from previous approaches.

## Key findings

- Proved optimal Lipschitz regularity of almost minimizers
- Established partial regularity of the free boundary
- Provided an alternative proof method using viscosity solutions

## Abstract

We consider almost minimizers to the one-phase energy functional and we prove their optimal Lipschitz regularity and partial regularity of their free boundary. These results were recently obtained by David and Toro, and David, Engelstein, and Toro. Our proofs provide a different method based on a non-infinitesimal notion of viscosity solutions.