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

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arxiv 2408.10019 v1 pith:WS5AWRAX submitted 2024-08-19 math.AP

Xavier Fernández-Real , Florian Gruen This is my paper · ORCID
classification math.AP
keywords boundarybernoullicontinuousminimizersone-phaseproblemregularityresults
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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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  1. Tangential touch between free and fixed boundaries for the fully nonlinear Alt-Phillips problem

    math.AP 2025-09 conditional novelty 7.0 of 10

    For the Alt-Phillips problem with γ in (1,2), the free boundary touches the fixed boundary tangentially wherever the Dirichlet data vanish, in the fully nonlinear and in the linear case.

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