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.
Stable cones in the Alt-Phillips free boundary problem
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abstract
In this paper we prove a classification result for axially symmetric one phase minimizers of the Alt-Phillips free boundary problem in dimensions 3, 4, and 5. To accomplish this, we establish a stability inequality that extends the one for the Alt-Caffarelli problem.
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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.