We consider a class of nonautonomous second order parabolic equations with unbounded coefficients defined in I × ℝ d , where I is a right-halfline. We prove logarithmic Sobolev and Poincaré inequalities with respect to an associated evolution system of measures {μ(t) : t ∈ I}, and we deduce hypercontractivity and asymptotic behavior results for the evolution operator G(t, s).
Hypercontractivity and Asymptotic Behavior in Nonautonomous Kolmogorov Equations / L., Angiuli; Lorenzi, Luca Francesco Giuseppe; Lunardi, Alessandra. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 38:12(2013), pp. 2049-2080. [10.1080/03605302.2013.840790]
Hypercontractivity and Asymptotic Behavior in Nonautonomous Kolmogorov Equations
LORENZI, Luca Francesco Giuseppe;LUNARDI, Alessandra
2013-01-01
Abstract
We consider a class of nonautonomous second order parabolic equations with unbounded coefficients defined in I × ℝ d , where I is a right-halfline. We prove logarithmic Sobolev and Poincaré inequalities with respect to an associated evolution system of measures {μ(t) : t ∈ I}, and we deduce hypercontractivity and asymptotic behavior results for the evolution operator G(t, s).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
