Log-Sobolev inequalities and hypercontractivity for Ornstein-Uhlenbeck evolution operators in infinite dimensions

2023/09/13 by Davide A. Bignamini, Bignamini, Davide A., Paolo De Fazio +1
Mathematics · Computer Science · Engineering · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2309.07319

Abstract

In an infinite dimensional separable Hilbert space X, we study the realizations of Ornstein-Uhlenbeck evolution operators \pst in the spaces L^p(X,\g_t), \\g_t\_t∈\R being the unique evolution system of measures for \pst in \R. We prove hyperconctractivity results, relying on suitable Log-Sobolev estimates. Among the examples we consider the transition evolution operator of a non autonomous stochastic parabolic PDE.

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