Stability of the Gaussian Faber–Krahn inequality

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2024年3月30日

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Alessandro Carbotti,
Simone Cito,
Domenico Angelo La Manna,
Diego Pallara

摘要

We prove a quantitative version of the Gaussian Faber–Krahn type inequality proved in (Betta et al. in Z. Angew. Math. Phys. 58:37–52, 2007) 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.