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Linear parabolic equations with strong singular potentials
Author(s):
Jerome
A.
Goldstein;
Qi
S.
Zhang
Journal:
Trans. Amer. Math. Soc.
355
(2003),
197-211.
MSC (2000):
Primary 35D05, 35K05, 35R25;
Secondary 35B50, 35C99, 35K15, 53C99
Posted:
August 1, 2002
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Abstract:
Using an extension of a recent method of Cabré and Martel (1999), we extend the blow-up and existence result in the paper of Baras and Goldstein (1984) to parabolic equations with variable leading coefficients under almost optimal conditions on the singular potentials. This problem has been left open in Baras and Goldstein. These potentials lie at a borderline case where standard theories such as the strong maximum principle and boundedness of weak solutions fail. Even in the special case when the leading operator is the Laplacian, we extend a recent result in Cabré and Martel from bounded smooth domains to unbounded nonsmooth domains.
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Additional Information:
Jerome
A.
Goldstein
Affiliation:
Department of Mathematics, University of Memphis, Memphis, Tennessee 38152
Email:
jgoldste@memphis.edu
Qi
S.
Zhang
Affiliation:
Department of Mathematics, University of California Riverside, Riverside, California 92521
Email:
qizhang@math.ucr.edu
DOI:
10.1090/S0002-9947-02-03057-X
PII:
S 0002-9947(02)03057-X
Received by editor(s):
July 22, 2001
Received by editor(s) in revised form:
January 17, 2002
Posted:
August 1, 2002
Copyright of article:
Copyright
2002,
American Mathematical Society
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