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.
Continuity up to the boundary for minimizers of the one-phase Bernoulli problem
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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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2025 1verdicts
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Tangential touch between free and fixed boundaries for the fully nonlinear Alt-Phillips problem
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.