# Lipschitz regularity of solutions to two-phase free boundary problems

## TL;DR

This paper establishes the Lipschitz continuity of viscosity solutions for a class of two-phase free boundary problems involving fully nonlinear operators, advancing understanding of solution regularity in complex free boundary scenarios.

## Contribution

It proves Lipschitz regularity for solutions to two-phase free boundary problems with fully nonlinear operators, a novel result in this area.

## Key findings

- Viscosity solutions are Lipschitz continuous.
- Regularity results apply to fully nonlinear operators.
- Advances understanding of free boundary problem solutions.

## Abstract

We prove Lipschitz continuity of viscosity solutions to a class of two-phase free boundary problems governed by fully nonlinear operators.