Overdetermined problems for the fractional Laplacian in exterior and annular sets

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...

Full description

Saved in:
Bibliographic Details
Published inJournal d'analyse mathématique (Jerusalem) Vol. 137; no. 1; pp. 101 - 134
Main Authors Soave, Nicola, Valdinoci, Enrico
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.03.2019
Subjects
Abstract Harmonic Analysis
Analysis
Dynamical Systems and Ergodic Theory
Functional Analysis
Mathematics
Mathematics and Statistics
Partial Differential Equations
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-018-0067-2