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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Green's matrices of second order elliptic systems with measurable coefficients in two dimensional domains


Authors: Hongjie Dong and Seick Kim
Journal: Trans. Amer. Math. Soc. 361 (2009), 3303-3323
MSC (2000): Primary 35A08, 35B65; Secondary 35J45
Published electronically: January 28, 2009
MathSciNet review: 2485428
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Abstract: We study Green's matrices for divergence form, second order strongly elliptic systems with bounded measurable coefficients in two dimensional domains. We establish existence, uniqueness, and pointwise estimates of Green's matrices.


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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, 262 Seongsanno, Seodaemun-gu, Seoul 120-749, Korea
Email: kimseick@yonsei.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04805-3
PII: S 0002-9947(09)04805-3
Keywords: Green function, Green's matrix, fundamental solution, fundamental matrix, second order elliptic system, measurable coefficients.
Received by editor(s): September 5, 2007
Published electronically: January 28, 2009
Additional Notes: The first author was partially supported by the National Science Foundation under agreement No. DMS-0111298 and a start-up funding from the Division of Applied Mathematics of Brown University.
The second author was supported by the Australian Research Council and by the New Faculty Research Grant No. 2008-1-0010 from Yonsei University.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.