黄新民.退化拟共形映射的整体同胚与二维奇异积分方程[J].数学研究及应用,1999,19(4):709~715
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
投稿时间:1996-10-14  
DOI:10.3770/j.issn:1000-341X.1999.04.015
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.
基金项目:广西壮族自治区教育厅自然科学基金资助课题(桂教科[1998]69号)
作者单位
黄新民 广西大学数学与信息科学系 
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中文摘要:
      设D是一个边界Г∈Ca1(0<a≤1)的有界单连通域,复函数q(z)∈Ca1,|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∈Ca1(0<a≤1),the complex function q(z)∈Ca1 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.
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