Stability of the Gaussian Faber-Krahn inequality

Published 8 Dec 2023 in math.AP | (2312.05146v2)

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.

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