Fundamental solutions for second-order parabolic systems with drift terms

Hongjie Dong; Seick Kim

doi:10.1090/proc/14004

Fundamental solutions for second-order parabolic systems with drift terms

Hongjie Dong, Seick Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 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 BMO_x⁻¹, under the assumption that weak solutions of the system satisfy a certain local boundedness estimate.

Original language	English
Pages (from-to)	3019-3029
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	7
DOIs	https://doi.org/10.1090/proc/14004
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

Access to Document

10.1090/proc/14004

Cite this

@article{6d2e16aee9d24d8191cb4b87fbf887d4,

title = "Fundamental solutions for second-order parabolic systems with drift terms",

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.",

author = "Hongjie Dong and Seick Kim",

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: {\textcopyright} 2018 American Mathematical Society.",

year = "2018",

month = jul,

doi = "10.1090/proc/14004",

language = "English",

volume = "146",

pages = "3019--3029",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "7",

}

TY - JOUR

T1 - Fundamental solutions for second-order parabolic systems with drift terms

AU - Dong, Hongjie

AU - Kim, Seick

N1 - 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.

PY - 2018/7

Y1 - 2018/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85045747227&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045747227&partnerID=8YFLogxK

U2 - 10.1090/proc/14004

DO - 10.1090/proc/14004

M3 - Article

AN - SCOPUS:85045747227

SN - 0002-9939

VL - 146

SP - 3019

EP - 3029

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 7

ER -

Fundamental solutions for second-order parabolic systems with drift terms

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this