A Faber-Krahn inequality for mixed local and nonlocal operators

We consider the first Dirichlet eigenvalue problem for a mixed local/nonlocal elliptic operator and we establish a quantitative Faber-Krahn inequality. More precisely, we show that balls minimize the first eigenvalue among sets of given volume and we provide a stability result for sets that almost a...

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Bibliographic Details
Published in:Journal d'analyse mathématique (Jerusalem) 2023-09, Vol.150 (2), p.405-448
Main Authors: Biagi, Stefano, Dipierro, Serena, Valdinoci, Enrico, Vecchi, Eugenio
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Analysis
Dirichlet problem
Dynamical Systems and Ergodic Theory
Eigenvalues
Functional Analysis
Mathematics
Mathematics and Statistics
Partial Differential Equations
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Summary:We consider the first Dirichlet eigenvalue problem for a mixed local/nonlocal elliptic operator and we establish a quantitative Faber-Krahn inequality. More precisely, we show that balls minimize the first eigenvalue among sets of given volume and we provide a stability result for sets that almost attain the minimum.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-023-0272-5