Electron. J. Diff. Equ., Vol. 2013 (2013), No. 72, pp. 1-11.

An approach for constructing coefficients of degenerate elliptic complex equations

Guo Chun Wen

Abstract:
This article deals with the inverse problem for degenerate elliptic systems of first order equations with Riemann-Hilbert type map in simply connected domains. Firstly the formulation and the complex form of the problem for the first-order elliptic systems with the degenerate rank 0 are given, and then the coefficients of the systems are constructed by a new complex analytic method. Here we verify and apply the Holder continuity of a singular integral operator.

Submitted November 30, 2012. Published March 17, 2013.
Math Subject Classifications: 35J55, 35R30, 47G10.
Key Words: Degenerate elliptic complex equations; coefficients of equations; method of integral equations; Holder continuity of a singular integral.

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Guo Chun Wen
LMAM, School of Mathematical Sciences
Peking University
Beijing 100871, China
email: Wengc@math.pku.edu.cn

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