# Continuity of the Free Boundary in a Problem involving the A-Laplacian

## TL;DR

This paper studies a two-dimensional free boundary problem with the A-Laplacian, demonstrating that the free boundary can be locally represented by continuous graphs, advancing understanding of boundary regularity in nonlinear PDEs.

## Contribution

It proves the local continuity of the free boundary in a problem involving the A-Laplacian, a novel result in nonlinear free boundary problems.

## Key findings

- The free boundary is locally represented by continuous graphs.
- The analysis advances understanding of boundary regularity for A-Laplacian problems.
- Provides foundational results for further regularity studies.

## Abstract

In this paper we investigate a two dimensional free boundary problem involving the A-Laplacian. We show that the free boundary is represented locally by graphs of a family of continuous functions.