Inserted: 8 jan 2019
Last Updated: 28 feb 2020
Journal: J. Funct. Anal.
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