A quantitative stability estimate for the fractional Faber-Krahn inequality
arXiv:1901.10845 · doi:10.1016/j.jfa.2020.108560
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.
36 pages. Corrected some misprints, references updated