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Global Properties of Transition Kernels Associated with Second-order Elliptic Operators

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Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 80)

Abstract

We study global regularity properties of transitions kernels associated with second-order differential operators in R N with unbounded drift and potential terms. Under suitable conditions, we prove Sobolev regularity of transition kernels and pointwise upper bounds. As an application, we obtain sufficient conditions implying the differentiability of the associated semigroup on the space of bounded and continuous functions on R N.

Keywords

Semigroups transition kernels parabolic regularity Lyapunov functions. 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Département de Mathématiques Faculté des SciencesUniversité Ferhat Abbes SétifSétifAlgeria
  2. 2.Dipartimento di Matematica “Ennio De Giorgi”Università di LecceLecceItaly
  3. 3.Dipartimento di Ingegneria dell’Informazione e Matematica ApplicataUniversità degli Studi di SalernoFisciano (Sa)Italy

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