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arXiv · 2409.17810

Qualitative properties of free boundaries for the exterior Bernoulli problem for the half Laplacian

Sven Jarohs·Tadeusz Kulczycki·Paolo Salani
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Abstract

In this work, we study the asymptotic behavior of the free boundary of the solution to the exterior Bernoulli problem for the half Laplacian when the Bernoulli's gradient parameter tends to $0^+$ and to $+\infty$. Moreover, we show that, under suitable conditions, the perpendicular rays of the free boundary always meet the convex envelope of the fixed boundary.

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Sven Jarohs, Tadeusz Kulczycki, Paolo Salani. 2024-09-26. Qualitative properties of free boundaries for the exterior Bernoulli problem for the half Laplacian. https://arxiv.org/abs/2409.17810

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