Fundamental solutions for second-order parabolic systems with drift terms

Hongjie Dong, Seick Kim

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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. We also establish Gaussian upper bounds for such fundamental solutions under the same conditions

Original languageEnglish
Pages (from-to)3019-3029
Number of pages11
JournalProceedings of the American Mathematical Society
Volume146
Issue number7
DOIs
Publication statusPublished - 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

Fingerprint Dive into the research topics of 'Fundamental solutions for second-order parabolic systems with drift terms'. Together they form a unique fingerprint.

Cite this