拟共形映射基本定理及复方程组的一类边值问题

THE FUNDAMENTAL THEOREM OF THE QUASICONFORMAL MAPPING AND A BOUN DARY VALUE PROBLEM FOR SYSTEM OF COMPLEX EQUATIONS

本文首先给出一阶复方程于单连通区域上拟共形映射的存在唯一性定理;然后讨论一阶线性椭圆型复方程组于多连通区域上的一类边值问题。

In this paper,we give firstly the fundamental theorem of the existenceand uniquenss of quasiconformal mapping for uniform elliptic complex equat-ion ω(?)=q^1(z)ω_z+q^2(z) (?) in a simply connected domain,and then discussthe solvability of a boundary value problem for linear system of complexequations of the first order w(?)=q^1(z)w_z+q^2(z)(?)+εf(z,w)+A^3(z),f(z,w)=A^1(z)w+A^2(z)(?) in a multiply connected domain,where w(z)=(w_1(z),…,w_m(z))~T,q^k(z)=(q_(ij)~k(z))_(mxm),A^k(z)=A_(ij)~k(z))_(mxm)(k=1,2),A^3(z)=(A_11~3(z),…,A_(m1)~3,(z))~T.