Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-22T21:02:44.696Z Has data issue: false hasContentIssue false

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
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
Get access

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

Type
Notes and Papers
Copyright
The London Mathematical Society 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)