Mappings of finite distortion: boundary extensions in uniform domains

被引：0
作者：
Tuomo Äkkinen
Chang-Yu Guo
机构：
[1] University of Jyväskylä,Department of Mathematics and Statistics
[2] University of Fribourg,Department of Mathematics
来源：
Annali di Matematica Pura ed Applicata (1923 -) | 2017年 / 196卷
关键词：
Quasiregular mappings; Mappings of finite distortion; Weighted capacity; Uniform domain; John domain; Radial limits; 30C65; 30C80; 31B15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider mappings on uniform domains with exponentially integrable distortion whose Jacobian determinants are integrable. We show that such mappings can be extended to the boundary, and moreover, these extensions are exponentially integrable with quantitative bounds. This extends previous results of Chang and Marshall (Am J Math 107(5):1015–1033, 1985) on analytic functions, Poggi-Corradini and Rajala (J Lond Math Soc (2) 76(2):531–544, 2007) and Äkkinen and Rajala [2] on mappings of bounded and finite distortion.
引用
收藏
页码：65 / 83
页数：18
相关论文
共 27 条
[1]  
Äkkinen T(2014)Radial limits of mappings of bounded and finite distortion J. Geom. Anal. 24 1298-1322
[2]  
Cianchi A(2008)Moser–Trudinger trace inequalities Adv. Math. 217 2005-2044
[3]  
Cianchi A(1996)A sharp embedding theorem for Orlicz–Sobolev spaces Indiana Univ. Math. J. 45 39-65
[4]  
Chang S-YA(1985)On a sharp inequality concerning the Dirichlet integral Am. J. Math. 107 1015-1033
[5]  
Marshall DE(1979)Uniform domains and the quasihyperbolic metric J. Anal. Math. 36 50-74
[6]  
Gehring FW(1976)Quasiconformally homogeneous domains J. Anal. Math. 30 172-199
[7]  
Osgood BG(2015)Uniform continuity of quasiconformal mappings onto generalized John domains Ann. Acad. Sci. Fenn. Math. 40 183-202
[8]  
Gehring FW(1996)Conformal capacity and the quasihyperbolic metric Indiana Univ. Math. J. 45 333-359
[9]  
Palka BP(1981)Quasiconformal mappings and extendability of functions in Sobolev spaces Acta Math. 147 71-88
[10]  
Guo CY(2008)Homeomorphisms of finite distortion: discrete length of radial images Math. Proc. Camb. Philos. Soc. 144 197-205
123