The Riemann-Hilbert problem for mixed complex equations of first order with degenerate rank 0

Abstract

This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed (ellipti-chyperbolic) complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem and prove the uniqueness of solutions for the boundary value problem. Afterwards, by using the method of successive iteration, the existence and estimates of solutions for the boundary value problem are verified. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order. In this article, the proof of Holder continuity of a singular double integer is very difficult and interesting as in this Section 4 below.