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Fundamental solutions for second-order parabolic systems with drift terms


Authors: Hongjie Dong and Seick Kim
Journal: Proc. Amer. Math. Soc. 146 (2018), 3019-3029
MSC (2010): Primary 35A08, 35K40; Secondary 35B45
DOI: https://doi.org/10.1090/proc/14004
Published electronically: February 28, 2018
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Abstract: We construct fundamental solutions of second-order parabolic systems of divergence form with bounded and measurable leading coefficients and divergence free first-order coefficients in the class of $ \mathrm {BMO}^{-1}_x$, under the assumption that weak solutions of the system satisfy a certain local boundedness estimate. We also establish Gaussian upper bounds for such fundamental solutions under the same conditions.


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Additional Information

Hongjie Dong
Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912
Email: hdong@brown.edu

Seick Kim
Affiliation: Department of Mathematics, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea
Email: kimseick@yonsei.ac.kr

DOI: https://doi.org/10.1090/proc/14004
Keywords: Fundamental solution, second order parabolic system, Gaussian estimate.
Received by editor(s): July 28, 2017
Received by editor(s) in revised form: October 9, 2017
Published electronically: February 28, 2018
Additional Notes: The first author was partially supported by the National Science Foundation under agreement DMS-1600593
The second author was partially supported by National Research Foundation of Korea under agreement NRF-2016R1D1A1B03931680.
Communicated by: Svitlana Mayboroda
Article copyright: © Copyright 2018 American Mathematical Society

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