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

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...

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Bibliographic Details
Main Authors Jarohs, Sven, Kulczycki, Tadeusz, Salani, Paolo
Format Journal Article
LanguageEnglish
Published 26.09.2024
Subjects
Mathematics - Analysis of PDEs
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Summary: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 meets the convex envelope of the fixed boundary.
DOI:10.48550/arxiv.2409.17810