# Global solutions to nonlinear two-phase free boundary problems

## TL;DR

This paper classifies all global Lipschitz solutions to certain two-phase free boundary problems governed by fully nonlinear equations, identifying them as either two-plane solutions or solutions to a one-phase problem.

## Contribution

It provides a complete classification of global solutions for a class of nonlinear two-phase free boundary problems, extending understanding of their structure.

## Key findings

- Global Lipschitz solutions are either two-plane solutions or one-phase solutions.
- Classification applies to problems governed by concave fully nonlinear equations.
- Results enhance understanding of free boundary problem solution structures.

## Abstract

We classify global Lipschitz solutions to two-phase free boundary problems governed by concave fully nonlinear equations, as either two-plane solutions or solutions to a one-phase problem.