Gaussian estimates for fundamental solutions of second order parabolic systems with time-independent coefficients
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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.References
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Additional Information
- Seick Kim
- Affiliation: Department of Mathematics, Yonsei University, 262 Seongsanno, Seodaemun-gu, Seoul 120-749, Korea
- MR Author ID: 707903
- Email: kimseick@yonsei.ac.kr
- Received by editor(s): April 20, 2005
- Received by editor(s) in revised form: November 3, 2006
- Published electronically: June 26, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 6031-6043
- MSC (2000): Primary 35A08, 35B45; Secondary 35K40
- DOI: https://doi.org/10.1090/S0002-9947-08-04485-1
- MathSciNet review: 2425701