Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations

Abstract

We consider a class of nonautonomous second order parabolic equations with unbounded coefficients defined in $I\times {\mathbb{R}}^d$, where $I$ is a right-halfline. We prove logarithmic Sobolev and Poincaré inequalities with respect to an associated evolution system of measures $\{{\mu }_t:t\in I\}$, and we deduce hypercontractivity and asymptotic behaviour results for the evolution operator $G(t,s)$.

Cited by in corpus (1)

• On the gradient estimates for evolution operators associated to Kolmogorov operators