English

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