Long time behavior of heat kernels of operators with unbounded drift terms

Given a second-order elliptic operator on Rd, with bounded diffusion coefficients and unbounded drift, which is the generator of a strongly continuous semigroup on L2(Rd) represented by an integral, we study the time behavior of the integral kernel and prove estimates on its decay at infinity. If th...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 377; no. 1; pp. 170 - 179
Main Authors Metafune, Giorgio, Ouhabaz, El Maati, Pallara, Diego
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.05.2011
Elsevier
Subjects
Analysis of PDEs
Exact sciences and technology
Functional Analysis
Group theory
Group theory and generalizations
Heat kernels
Mathematical analysis
Mathematics
Parabolic operators
Sciences and techniques of general use
Unbounded coefficients
Heat kernels
Parabolic operators
Unbounded coefficients
Second order
Mathematical analysis
Heat kernel
Bounded operator
Elliptic operator
Semigroup
unbounded drifts
heat kernels
parabolic operators
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Summary:Given a second-order elliptic operator on Rd, with bounded diffusion coefficients and unbounded drift, which is the generator of a strongly continuous semigroup on L2(Rd) represented by an integral, we study the time behavior of the integral kernel and prove estimates on its decay at infinity. If the diffusion coefficients are symmetric, a local lower estimate is also proved.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2010.10.023