Publication

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

Xavier Fernandez-Real Girona
2025

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 Hölder-continuous boundary data. As an application, we use them to extend recent generic uniqueness and regularity results to families of continuous functions.

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

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