Calculus of Variations and Geometric Measure Theory
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L. Brasco - E. Cinti - S. Vita

A quantitative stability estimate for the fractional Faber-Krahn inequality

created by brasco on 08 Jan 2019



Inserted: 8 jan 2019
Last Updated: 8 jan 2019

Pages: 35
Year: 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


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