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Stable cones in the Alt-Phillips free boundary problem

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arxiv 2403.13059 v2 pith:F5ZUIYCT submitted 2024-03-19 math.AP

Aram Karakhanyan , Tomás Sanz-Perela This is my paper
classification math.AP
keywords problemalt-phillipsboundaryfreeaccomplishalt-caffarelliaxiallyclassification
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Smoothness and stability in the Alt-Phillips problem

    math.AP 2025-07 conditional novelty 8.0 of 10

    For the Alt-Phillips free boundary problem, the paper proves smoothness of regular free boundaries for all exponents, derives a stability inequality for negative exponents, and rules out nontrivial axially symmetric s...

  2. 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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