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Parabolic Problems pp 415–432Cite as

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.

Mathematics Subject Classification (2000). Primary 35K65; Secondary 47D07, 60J35.

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Author information

Authors and Affiliations

  1. Département de Mathématiques Faculté des Sciences, Université Ferhat Abbes Sétif, Route de Scipion, 19000, Sétif, Algeria

    Karima Laidoune

  2. Dipartimento di Matematica “Ennio De Giorgi”, Università di Lecce, C.P.193, I-73100, Lecce, Italy

    Giorgio Metafune & Diego Pallara

  3. Dipartimento di Ingegneria dell’Informazione e Matematica Applicata, Università degli Studi di Salerno, Via Ponte Don Melillo, I-84084, Fisciano (Sa), Italy

    Abdelaziz Rhandi

Authors
  1. Karima Laidoune
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  2. Giorgio Metafune
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  3. Diego Pallara
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  4. Abdelaziz Rhandi
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Corresponding author

Correspondence to Karima Laidoune .

Editor information

Editors and Affiliations

  1. Inst. Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, Hannover, 30167, Germany

    Joachim Escher

  2. School of Physical Sciences, Dept. Mathematics, University of California, Irvine, Irvine, 92697-3875, California, USA

    Patrick Guidotti

  3. , Fachbereich Mathematik, TU Darmstadt, Schlossgartenstr 7, Darmstadt, 64289, Germany

    Matthias Hieber

  4. Inst. Applied Mathematics & Mechanics, Warsaw University, ul. Banacha 2, Warszawa, 02-097, Poland

    Piotr Mucha

  5. , FB Mathematik und Informatik, Universität Halle-Wittenberg, Theodor-Lieser-Strasse 5, Halle, 06099, Germany

    Jan W. Prüss

  6. 3-4-1, Ohkubo Shinjuku-ku, Tokyo, 169-8555, Japan

    Yoshihiro Shibata

  7. , Deparment of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA

    Gieri Simonett

  8. Inst. Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, Hannover, 30167, Germany

    Christoph Walker

  9. Fac. Mathematics & Information Sciences, Warsaw University of Technology, pl. Politechniki 1, Warszawa, 00-661, Poland

    Wojciech Zajaczkowski

Additional information

Dedicated to Prof. H. Amann on the occasion of his 70th birthday

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Laidoune, K., Metafune, G., Pallara, D., Rhandi, A. (2011). Global Properties of Transition Kernels Associated with Second-order Elliptic Operators. In: , et al. Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 80. Springer, Basel. https://doi.org/10.1007/978-3-0348-0075-4_21

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