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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.

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

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Correspondence to Karima Laidoune .

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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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