Existence of Solutions of Inverse Problems for Elliptic Complex Equations with Degenerate Curve in Multiple Connected Domains

Abstract

The present paper deals with the inverse problem for degenerate elliptic systems of first order equations in multiple connected domains with Riemann-Hilbert type map. Firstly the formulation and the complex form of the problem for the degenerate elliptic systems of first order are given, and then the coefficients of the above systems are constructed by a new complex analytic method. As an application of the above results, we can derive the corresponding results of the inverse problem for degenerate elliptic equations of second order in multiple connected domains from Dirichlet to Neumann map.