Accepted Paper

Inserted: 8 dec 2023
Last Updated: 22 feb 2024

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

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.

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

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