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arXiv · 2611.08670

Non-conical classical solutions to the one-phase free boundary problem with an isolated singularity

Minyoung Jeong
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Abstract

Several examples of one-homogeneous classical solutions to the one-phase free boundary problem with an isolated free boundary singularity are known. Adapting the approach of Caffarelli, Hardt, and Simon for minimal surfaces, we construct non-conical classical solutions with an isolated free boundary singularity by perturbing a one-homogeneous solution $U$. Moreover, if $U$ is strictly stable (respectively, non-degenerate), then any solution sufficiently close to $U$ is also strictly stable (respectively, non-degenerate).

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Minyoung Jeong. 2026-11-05. Non-conical classical solutions to the one-phase free boundary problem with an isolated singularity. https://arxiv.org/abs/2611.08670

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