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arXiv · 1901.10845

A quantitative stability estimate for the fractional Faber-Krahn inequality

Lorenzo Brasco·Eleonora Cinti·Stefano Vita
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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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Lorenzo Brasco, Eleonora Cinti, Stefano Vita. 2019-01-30. A quantitative stability estimate for the fractional Faber-Krahn inequality. https://doi.org/10.1016/j.jfa.2020.108560

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