Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations

Details Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations

2012-03-06

arxiv.org/abs/1203.1280v1

Mathematics

Analysis of PDEs

Scientific paper

We consider a class of nonautonomous second order parabolic equations with unbounded coefficients defined in $I\times\R^d$, where $I$ is a right-halfline. We prove logarithmic Sobolev and Poincar\'e 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 $G(t,s)$.

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