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.
Brasco, L., Cinti, E., Vita, S. (2020). A quantitative stability estimate for the fractional Faber-Krahn inequality. JOURNAL OF FUNCTIONAL ANALYSIS, 279(3) [10.1016/j.jfa.2020.108560].
A quantitative stability estimate for the fractional Faber-Krahn inequality
Vita, S
2020
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.
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