A NEW METHOD FOR CONSTRUCTING COEFFICIENTS OF ELLIPTIC COMPLEX EQUATIONS WITH RIEMANN-HILBERT TYPE MAP

摘要

The present paper mainly concerns the inverse problem for linear elliptic complex equations of first order with Riemann-Hilbert type map in simply connected domains. Firstly the formulation and the complex form of the problem for the equations are given, and then the existence of solutions for the above problem is proved by a new complex analytic method, where the advantage of the other methods is absorbed, and the used method in this paper is more simple and the obtained result is more general. As an application of the above results, we can derive the corresponding results of the inverse problem for second order elliptic equations from Dirichlet to Neumann map.