Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 72, pp. 1-11.

Title: An approach for constructing coefficients of degenerate elliptic 
       complex equations
        
Author: Guo Chun Wen (Peking Univ., Beijing, China)

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.