Overdetermined problems for the fractional Laplacian in exterior and annular sets

Nicola Soave, Enrico Valdinoci

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We consider a fractional elliptic equation in an unbounded set with both Dirichlet and fractional normal derivative datum prescribed. We prove that the domain and the solution are necessarily radially symmetric. We also study the extension of the result in bounded non-convex regions, as well as the radial symmetry of the solution when the set is assumed a priori to be rotationally symmetric.

Original languageEnglish
Pages (from-to)101-134
Number of pages34
JournalJournal d'Analyse Mathematique
Volume137
Issue number1
DOIs
Publication statusPublished - Mar 2019

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Overdetermined Problems
Fractional Laplacian
Fractional
Radial Symmetry
Elliptic Equations
Dirichlet
Derivative

Cite this

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abstract = "We consider a fractional elliptic equation in an unbounded set with both Dirichlet and fractional normal derivative datum prescribed. We prove that the domain and the solution are necessarily radially symmetric. We also study the extension of the result in bounded non-convex regions, as well as the radial symmetry of the solution when the set is assumed a priori to be rotationally symmetric.",
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Overdetermined problems for the fractional Laplacian in exterior and annular sets. / Soave, Nicola; Valdinoci, Enrico.

In: Journal d'Analyse Mathematique, Vol. 137, No. 1, 03.2019, p. 101-134.

Research output: Contribution to journalArticle

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AU - Valdinoci, Enrico

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AB - We consider a fractional elliptic equation in an unbounded set with both Dirichlet and fractional normal derivative datum prescribed. We prove that the domain and the solution are necessarily radially symmetric. We also study the extension of the result in bounded non-convex regions, as well as the radial symmetry of the solution when the set is assumed a priori to be rotationally symmetric.

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