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ON ARONSON'S UPPER BOUNDS FOR HEAT KERNELS

Published online by Cambridge University Press:  24 March 2003

RICHARD F. BASS
RICHARD F. BASS
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA bass@math.uconn.edu
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Abstract

Let ${\cal L}$ be a uniformly elliptic operator in divergence form on ${\bb R}^d$, and let $p(t,x,y)$ be the fundamental solution to the heat equation for ${\cal L}$. A new proof is given of Aronson's upper bound:\[p(t,x,y)\le c_1t^{-d/2}\exp(-c_2|x-y|^2/t).\]

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Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 4 , July 2002 , pp. 415 - 419
Copyright
© The London Mathematical Society 2002

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