Continuity up to the boundary for minimizers of the one-phase Bernoulli problem

TL;DR

This paper establishes new boundary regularity results for minimizers of the one-phase Bernoulli problem with continuous boundary data, enabling extensions of uniqueness and regularity results to broader function families.

Contribution

It provides novel boundary regularity theorems for the Bernoulli problem with continuous and Hölder boundary data, advancing understanding of free boundary regularity.

Findings

Boundary regularity results for continuous boundary data.

Extension of uniqueness results to continuous boundary functions.

Enhanced regularity understanding for the Bernoulli free boundary problem.

Abstract

We prove new boundary regularity results for minimizers to the one-phase Alt-Caffarelli functional (also known as Bernoulli free boundary problem) in the case of continuous and H\"older-continuous boundary data. As an application, we use them to extend recent generic uniqueness and regularity results to families of continuous functions.