A. Colesanti

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math.AP2026

Geometric properties of solutions to elliptic PDE's in Gauss space and related Brunn-Minkowski type inequalities

Andrea Colesanti, Lei Qin, Paolo Salani

We prove a Brunn-Minkowski type inequality for the first (nontrivial) Dirichlet eigenvalue of the weighted $p$ -operator \[ -Î_{p,Î³}u=-\text{div}(|\nabla u|^{p-2} \nabla u)+(x,\na…

math.AP2024

The Brunn-Minkowski inequality for the first eigenvalue of the Ornstein-Uhlenbeck operator and log-concavity of the relevant eigenfunction

Andrea Colesanti, Elisa Francini, Galyna Livshyts +1

We prove that the first (nontrivial) Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator $L (u) = I^ u - ⟨ \nabla u, x ⟩,$ as a function of the domain, is convex with…