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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Linear parabolic equations with strong singular potentials


Authors: Jerome A. Goldstein and Qi S. Zhang
Journal: Trans. Amer. Math. Soc. 355 (2003), 197-211
MSC (2000): Primary 35D05, 35K05, 35R25; Secondary 35B50, 35C99, 35K15, 53C99
Published electronically: August 1, 2002
MathSciNet review: 1928085
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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: https://doi.org/10.1090/S0002-9947-02-03057-X
Received by editor(s): July 22, 2001
Received by editor(s) in revised form: January 17, 2002
Published electronically: August 1, 2002
Article copyright: © Copyright 2002 American Mathematical Society