Calculus of Variations and Geometric Measure Theory

L. Brasco - E. Cinti - S. Vita

A quantitative stability estimate for the fractional Faber-Krahn inequality

created by brasco on 08 Jan 2019
modified on 28 Feb 2020


Accepted Paper

Inserted: 8 jan 2019
Last Updated: 28 feb 2020

Journal: J. Funct. Anal.
Pages: 36
Year: 2020


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 $1$.

Keywords: fractional Laplacian, Stability of eigenvalues