Stability of the Gaussian Faber-Krahn inequality

2023/12/08 by Alessandro Carbotti, Carbotti, Alessandro, Simone Cito +5 · 2 citations
Mathematics · #35P15 #49R05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2312.05146

openalex publication_date 2023/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a quantitative version of the Gaussian Faber-Krahn type inequality proved by Betta, Chiacchio and Ferone for the first Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator, estimating the deficit in terms of the Gaussian Fraenkel asymmetry. As expected, the multiplicative constant only depends on the prescribed Gaussian measure.

Cited by

• The Polya-Szego principle in the fractional setting: a glimpse on nonlocal functional inequalities
• The strong log-concavity for first eigenfunction of the Ornstein-Uhlenbeck operator in the class of convex bodies

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