退化拟共形映射的整体同胚与二维奇异积分方程

The Degenerate Quasicomformal Global Homeomorphism and Two Dimensional Singular Integral Equations

中文关键词:  退化  拟共形映射  整体同胚  二维  奇异积分方程

英文关键词:degenerate  quasicomformal mapping  global homeomorphism  two dimensional  singular integral equations.

中文摘要:

      设Ｄ是一个边界Г∈C_a¹（０＜a≤１）的有界单连通域，复函数ｑ（ｚ）∈C_a¹，|ｑ（ｚ）|≤１，等式只能在Г上成立，且在Г上等式ｑ（ｚ（ｔ）)ｚ′（ｔ）/ｚ′（ｔ）+1|_z∈Г＝０最多在有限个点上成立．本文给出了复伸张ｑ（ｚ）满足上述条件时的退化拟共形映射的整体同胚解及以ｑ（ｚ）为系数的一类二维奇异积分方程的解．

英文摘要:

      Suppose that D is a simply connected region whose boundary Г∈C_a¹（０＜a≤１）,the complex function ｑ（ｚ）∈C_a¹ and |ｑ（ｚ）|≤１, the strict form may only be hold for z∈Γ, and equality ｑ（ｚ（ｔ）)ｚ′（ｔ）/ｚ′（ｔ）+1|_z∈Г＝０ may hold only at finite points. In this paper global homeomorphism solutions of a Beltrami equation with the complex dilation q(z) satisfy above conditions and solutions of a kind of two dimensional singular integral equations with the coefficient q(z) were btained.