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

Xavier Fernández-Real; Florian Gruen

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arXiv · 2408.10019

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

Xavier Fernández-Real·Florian Gruen

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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.

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Xavier Fernández-Real, Florian Gruen. 2024-08-19. Continuity up to the boundary for minimizers of the one-phase Bernoulli problem. https://arxiv.org/abs/2408.10019

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