The strong log-concavity for first eigenfunction of the Ornstein-Uhlenbeck operator in the class of convex bodies
Abstract
In this paper, we prove that the first (positive) Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator \[ L(u)= u-(∇ u,x), \] is strongly log-concave if the domain is bounded and convex, which improves the conclusion in [6]. We also provide a characterization of the equality case of the Brunn-Minkowski inequality for the principal frequency of L(u) in the class of convex bodies.
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