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

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.