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arXiv · 1203.1280

Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations

L. Angiuli·L. Lorenzi·A. Lunardi
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Abstract

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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L. Angiuli, L. Lorenzi, A. Lunardi. 2012-03-06. Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations. https://arxiv.org/abs/1203.1280

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