Hypercontractivity and Asymptotic Behavior in Nonautonomous Kolmogorov Equations

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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Veröffentlicht in:Communications in partial differential equations 2013-12, Vol.38 (12), p.2049-2080
Hauptverfasser: Angiuli, Luciana, Lorenzi, Luca, Lunardi, Alessandra
Format: Artikel
Sprache:eng
Schlagworte:
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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Zusammenfassung: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).
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2013.840790