A quantitative stability estimate for the fractional Faber-Krahn inequality
Analysis of PDEs
2021-03-12 v2 Optimization and Control
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.
Keywords
Cite
@article{arxiv.1901.10845,
title = {A quantitative stability estimate for the fractional Faber-Krahn inequality},
author = {Lorenzo Brasco and Eleonora Cinti and Stefano Vita},
journal= {arXiv preprint arXiv:1901.10845},
year = {2021}
}
Comments
36 pages. Corrected some misprints, references updated