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 BMOx−1, under the assumption that weak solutions of the system satisfy a certain local boundedness estimate.
Original language | English |
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Pages (from-to) | 3019-3029 |
Number of pages | 11 |
Journal | Proceedings of the American Mathematical Society |
Volume | 146 |
Issue number | 7 |
DOIs | |
Publication status | Published - 2018 Jul |
Bibliographical note
Funding Information:Received by the editors July 28, 2017, and, in revised form, October 9, 2017. 2010 Mathematics Subject Classification. Primary 35A08, 35K40; Secondary 35B45. Key words and phrases. Fundamental solution, second order parabolic system, Gaussian estimate. 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.
Publisher Copyright:
© 2018 American Mathematical Society.
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics