We prove a quantitative version of the Faber-Krahn inequality for the first eigenvalue of the fractional Dirichlet-Laplacian of order s. This is done by using the so-called Caffarelli-Silvestre extension and adapting to the nonlocal setting a trick by Hansen and Nadirashvili. The relevant stability estimate comes with an explicit constant, which is stable as the fractional order of differentiability goes to 1.

A quantitative stability estimate for the fractional Faber-Krahn inequality

Brasco L.;Cinti E.;Vita S.
2020-01-01

Abstract

We prove a quantitative version of the Faber-Krahn inequality for the first eigenvalue of the fractional Dirichlet-Laplacian of order s. This is done by using the so-called Caffarelli-Silvestre extension and adapting to the nonlocal setting a trick by Hansen and Nadirashvili. The relevant stability estimate comes with an explicit constant, which is stable as the fractional order of differentiability goes to 1.
2020
279
3
1
49
Fractional Laplacian; Stability of eigenvalues
Brasco L.; Cinti E.; Vita S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1847424
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