Inserted: 8 jan 2019
Last Updated: 8 jan 2019
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