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. We also establish Gaussian upper bounds for such fundamental solutions under the same conditions
Bibliographical noteFunding 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.
© 2018 American Mathematical Society.
All Science Journal Classification (ASJC) codes
- Applied Mathematics