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Archiv der Mathematik

, Volume 94, Issue 6, pp 565–577 | Cite as

Time dependent Lyapunov functions for some Kolmogorov semigroups perturbed by unbounded potentials

  • Aissa Aibeche
  • Karima Laidoune
  • Abdelaziz Rhandi
Article

Abstract

We study global regularity properties of transition kernels associated to second order differential operators in \({\mathbb {R}^N}\) with unbounded drift and potential terms. Under suitable conditions, we prove pointwise upper bounds. We use time dependent Lyapunov function techniques allowing us to gain a better time behaviour of such kernels.

Mathematics Subject Classification (2000)

Primary 35K65 47D07 Secondary 60J35 

Keywords

Kolmogorov semigroups Kernel estimates Lyapunov functions Schrödinger operators 

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Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  • Aissa Aibeche
    • 1
  • Karima Laidoune
    • 1
  • Abdelaziz Rhandi
    • 2
  1. 1.Département de Mathématiques, Faculté des SciencesUniversité Ferhat Abbes SétifSétifAlgeria
  2. 2.Dipartimento di Ingegneria dell’Informazione e Matematica ApplicataUniversità degli Studi di SalernoFisciano (Sa)Italy

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