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ESTIMATES OF HEAT KERNELS FOR A CLASS OF SECOND-ORDER ELLIPTIC OPERATORS WITH APPLICATIONS TO SEMI-LINEAR INEQUALITIES IN EXTERIOR DOMAINS

Published online by Cambridge University Press:  28 January 2004

VLADIMIR KONDRATIEV ,
VITALI LISKEVICH ,
ZEEV SOBOL  and
OLEKSIY US
VLADIMIR KONDRATIEV
Affiliation:
Department of Mathematics and Mechanics, Moscow State University, Moscow 119 899, Russia
VITALI LISKEVICH
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW
ZEEV SOBOL
Affiliation:
Department of Mathematics, Imperial College, London SW7 2BZ
OLEKSIY US
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW
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Abstract

Fundamental solutions to second-order parabolic and elliptic equations with lower-order terms are studied. New sufficient conditions on the coefficients of the lower-order terms are given that guarantee the validity of two-sided Gaussian bounds on the fundamental solution to the parabolic equation, locally and globally in time. As an application, the problem of existence and non-existence of positive solutions to a class of semi-linear equations is studied.

Keywords

35K1035J60
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 107 - 127
Copyright
The London Mathematical Society 2004

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