一阶非线性椭圆型复方程的非线性P-H边值问题

Nonlinear Boundary Value Problem of R--H Type for a Nonlinear Elliptic Systems of First Order in the Plane

本文运用与 Newton迭代相结合的嵌入方法,讨论了一类在2n+1个附加条件下的一般非线性椭圆型复方程的非线性Riemann-Hilbert边值问题.我们在C^(1+α)(D)上得到了解的存在性与唯一性,并给出了近似解的误差估计式。

In this paper, by using an embedding method combined withNewton iteration procedure we discuss a class of nonlinear Riemann--Hilbertboundary value problem with 2n+1 additional conditions for a nonlinearelliptic system of first order in the plane. For this problem, the existenceand uniqueness of solution in C^(1+)(D) is established. An error estimate ofapproximating solution is also obtained.