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arXiv · 2610.40232

The fractional Faber--Krahn inequality in sharp quantitative form

Michael Goldman·Matteo Novaga·Berardo Ruffini
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Abstract

We prove that the first Dirichlet eigenvalue of the fractional Laplacian satisfies the sharp quantitative Faber--Krahn inequality. This was conjectured by Brasco, Cinti and Vita, who proved the inequality with a sub-optimal exponent. The proof adapts to the non-local setting the level-set argument recently introduced by Guerra, Machado and Ramos for the Laplacian. It is carried out on the horizontal level sets of the Caffarelli--Silvestre extension of the torsion function, where the asymmetry appears only as a boundary value at the corner of the extension variables.

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Michael Goldman, Matteo Novaga, Berardo Ruffini. 2026-10-29. The fractional Faber--Krahn inequality in sharp quantitative form. https://arxiv.org/abs/2610.40232

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