Kernel estimates for a class of Kolmogorov semigroups
type: Item
instance of: scholarly article
title: Kernel estimates for a class of Kolmogorov semigroups
zbMATH Open document ID: 1161.47028
author: Chiara Spina
published in: Archiv der Mathematik
publication date: 2009-01-29T00:00:00Z
review text: Let \(A:=\sum_{i,j=1}^N a_{ij} D_{ij}+\sum_{i=1}^NF_i D_i\) be a second order partial differential operator with bounded coefficients \((a_{ij})_{i,j=1}^N\), but unbounded drift. Under some mild restriction on the smoothness of the coefficients and ellipticity of \((a_{ij})_{i,j=1}^N\), it is proved that the heat kernel associated with \(A\) can be estimated from above as follows: \[ p(t,x,y)\leq c(t) w(y,t), \] where \(w(t,y)\) is a Lyapunov function for the operator \(\partial_t+A\). Such results are related to [\textit{G.\,Metafune, D.\,Pallara} and \textit{A.\,Rhandi}, ``Global properties of transition probabilities of singular diffusions'', Theor.\ Probab.\ Appl.\ (to appear)].
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 5500565
zbMATH Keywords: transition semigroups
zbMATH Keywords: transition probabilities
zbMATH Keywords: Lyapunov function
reviewed by: V. Knopova
MaRDI profile type: Publication
full work available at URL: s00013-008-2676-y
OpenAlex ID: W2061221056
DOI: 10.1007/S00013-008-2676-Y
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description: scientific article; zbMATH DE number 5500565