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• W3089264384 abstract "The aim of this work is to study homogeneous stable to the thin (or fractional) one-phase free boundary problem. The problem of classifying stable (or minimal) homogeneous in dimensions $ngeq3$ is completely open. In this context, axially symmetric are expected to play the same role as Simons' cone in the classical theory of minimal surfaces, but even in this simpler case the problem is open. The goal of this paper is twofold. On the one hand, our first main contribution is to find, for the first time, the stability condition for the thin one-phase problem. Quite surprisingly, this requires the use of large solutions for the fractional Laplacian, which blow up on the free boundary. On the other hand, using our new stability condition, we show that any axially symmetric homogeneous stable solution in dimensions $nle 5$ is one-dimensional, independently of the parameter $sin (0,1)$." @default.
• W3089264384 created "2020-10-01" @default.
• W3089264384 creator A5005248507 @default.
• W3089264384 creator A5007518239 @default.
• W3089264384 date "2020-09-24" @default.
• W3089264384 modified "2023-09-27" @default.
• W3089264384 title "Stable cones in the thin one-phase problem." @default.
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• W3089264384 hasPublicationYear "2020" @default.
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