# Thin One-Phase almost minimizers

## TL;DR

This paper establishes optimal regularity results for almost minimizers of the thin-one phase energy functional and introduces a viscosity solutions approach to analyze their free boundary behavior.

## Contribution

It extends the regularity theory from energy minimizers to almost minimizers using a novel viscosity solutions framework.

## Key findings

- Proves optimal regularity of solutions.
- Establishes partial regularity of the free boundary.
- Adapts viscosity solutions methods to this setting.

## Abstract

We consider almost minimizers to the thin-one phase energy functional and we prove optimal regularity of the solution and partial regularity of the free boundary. We thus recover the theory for energy minimizers. Our methods are based on a noninfinitesimal notion of viscosity solutions.