距离边界条件域和Hlder连续性  

Distance boundary condition domains and Hlder continuity

作　　者：伍接朝[1] 王芳[2] 

机构地区：[1]长沙理工大学计算机与通信工程学院,湖南长沙410076 [2]长沙理工大学数学与计算科学学院,湖南长沙410076

出　　处：《长沙交通学院学报》2007年第2期85-88,共4页Journal of Changsha Communications University

基　　金：湖南省自然科学基金资助项目(05JJ30013)

摘　　要：主要利用距离边界条件域和Hlder连续性的定义,当kD(x1,x2),jD(x1,x2)满足一定条件后,得到了拟共形映射和Hlder连续性之间的4个充要条件和1个充分条件,即设D是-Rn中的k-BC域,f是Rn中D→D′的K拟共形映射,则f在D中的任一开球B上是Hlder连续的,当且仅当D′=f(D)是k-BC域;设D是-Rn中的有界一致域,f是Rn中D→D′的K拟共形映射,则f在D上是Hlder连续的,当且仅当D′=f(D)是k-BC域;设D是-Rn中的有界一致域,f是-Rn中D→D′的K拟共形映射,则f在D上是Hlder连续的,当且仅当D′=f(D)是j-BC域;有界一致域D是-Rn中的K拟共形不变量,当且仅当f在D上是H lder连续的;设D是-Rn中的一致域和j-BC域,则D是-Rn中的John域.This paper utilizes the definition of distance boundary condition domains and Hoelder continuitiy, obtains four necessary and sufficient conditions and one sufficient condition of quasiconformal mapping and Hoelder continuity when ko （x1 ,x2 ） and jD （x1,x2） satisfies some conditions. If D is a k-BC domian in R^n and f is a K-quasiconformal mapping from D to D＇ ,thenf is Hoelder continuous in each open ball contained in D if and only if D＇ =f（D） is a k-BC domain;if D is a bounded uniform domain in R^n and f is a K-quasiconformal mapping from D to D＇,thenfis Hoelder continuous in D if and only if D＇ =f（D） is a k-BC domain; ifD is a bounded uniform domain and f is a K-quasiconformal mapping, then f is Hoelder continuous in D if and only if D＇ =f（D） is a j-BC domain; a bounded uniform domain D is invariant for quasiconformal mapping if and only iff is Hoelder continuous in D; if D is a uniform domain and j-BC domain ,then D is a John domain in R^n.

关 键 词：拟共形映射 拟双曲距离 拟双曲边界条件 Hoeder连续性 

分 类 号：O174.55[理学—数学]