Hypercontractivity and Asymptotic Behavior in Nonautonomous Kolmogorov Equations

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 hypercont...

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Bibliographic Details
Published inCommunications in partial differential equations Vol. 38; no. 12; pp. 2049 - 2080
Main Authors Angiuli, Luciana, Lorenzi, Luca, Lunardi, Alessandra
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis Group 02.12.2013
Taylor & Francis Ltd
Subjects
Asymptotic behavior
Asymptotic properties
Brownian motion
Evolution
Evolution operators
Hypercontractivity
Inequalities
Logarithmic Sobolev inequality
Mathematical analysis
Nonautonomous second order elliptic operators
Operators
Partial differential equations
Probability
Unbounded coefficients
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Summary: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).
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2013.840790