Applications of method of integral equations and integral operators to Riemann-Hilbert problem for elliptic complex equations of first order

Guochun Wen and Yanhui Zhang

Abstract

In this arti le, we first propose the Riemann-Hilbert problem for uniformly elliptic complex equations of rst order and its well-posedness. Then we give the integral representation of solutions of RiemannHilbert problem for the omplex equations. Moreover we shall obtain a priori estimates of solutions of the modied Riemann-Hilbert problem and verify its solvability by the method of integral equations. Finally the solvability results of the original boundary value problem an be obtained..