平面非线性椭圆型方程组的非线性斜微商问题

NONLINEAR OBLIQUE DERIVATIVE PROBLEMS FOR A NONLINEAR ELLIPTIC SYSTEMS OF FIRST ORDER IN THE PLANE

本文研究平面一阶非线性椭圆型复方程W_z=H(z,W,W_z)具有非线性边值条件Re[z^(-n)W_z]=γ(z,W)的斜微商问题。在空间C^(1+α)(G)中,利用与Newton迭代相结合的嵌入方法证明了在某些假设与附加条件下其解的存在性与唯一性。

This paper deals with the nonlinear oblique derivative problems for the following system W_z=H(z,w,W_z),z∈G where G is a unit disk. By using an embedding method combined with Newton iteration procedure, a proof is presented for the existence and uniqueness of the solution in C^(1+a)(G) to these boundary value problems under some hypothese and additional conditions.