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Transactions of the American Mathematical Society

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



On A parabolic equation with a singular lower order term

Author: Qi Zhang
Journal: Trans. Amer. Math. Soc. 348 (1996), 2811-2844
MSC (1991): Primary 35K10
MathSciNet review: 1360232
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Abstract: We obtain the existence of the weak Green's functions of parabolic equations with lower order coefficients in the so called parabolic Kato class which is being proposed as a natural generalization of the Kato class in the study of elliptic equations. As a consequence we are able to prove the existence of solutions of some initial boundary value problems. Moreover, based on a lower and an upper bound of the Green's function, we prove a Harnack inequality for the non-negative weak solutions.

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Qi Zhang
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Received by editor(s): September 26, 1994
Received by editor(s) in revised form: May 28, 1995
Article copyright: © Copyright 1996 American Mathematical Society