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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Gaussian estimates for fundamental solutions of second order parabolic systems with time-independent coefficients


Author: Seick Kim
Journal: Trans. Amer. Math. Soc. 360 (2008), 6031-6043
MSC (2000): Primary 35A08, 35B45; Secondary 35K40
Published electronically: June 26, 2008
MathSciNet review: 2425701
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Abstract: Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on $ \mathbb{R}^n$. In particular, in the case when $ n=2$ they obtained Gaussian upper bound estimates for the heat kernel without imposing further assumption on the coefficients. We study the fundamental solutions of the systems of second order parabolic equations in the divergence form with bounded, measurable, time-independent coefficients, and extend their results to the systems of parabolic equations.


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Additional Information

Seick Kim
Affiliation: Department of Mathematics, Yonsei University, 262 Seongsanno, Seodaemun-gu, Seoul 120-749, Korea
Email: kimseick@yonsei.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04485-1
PII: S 0002-9947(08)04485-1
Keywords: Gaussian estimates, a priori estimates, parabolic system
Received by editor(s): April 20, 2005
Received by editor(s) in revised form: November 3, 2006
Published electronically: June 26, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.