Calculus of Variations and Geometric Measure Theory

A. Carbotti - S. Cito - D. A. La Manna - D. Pallara

Stability of the Gaussian Faber-Krahn inequality

created by carbotti on 08 Dec 2023
modified on 04 May 2024


Published Paper

Inserted: 8 dec 2023
Last Updated: 4 may 2024

Journal: Annali di Matematica Pura e Applicata
Pages: 16
Year: 2023

ArXiv: 2312.05146 PDF


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.

Keywords: first Dirichlet eigenvalue, Gaussian analysis, Faber-Krahn inequality, Ornstein-Uhlenbeck Operator