Mappings of finite distortion: boundary extensions in uniform domains

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• 作者：Tuomo Äkkinen ; Chang-Yu Guo
• 关键词：Quasiregular mappings ; Mappings of finite distortion ; Weighted capacity ; Uniform domain ; John domain ; Radial limits
• 刊名：Annali di Matematica Pura ed Applicata (1923 -)
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：196
• 期：1
• 页码：65-83
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Berlin Heidelberg
• ISSN：1618-1891
• 卷排序：196

文摘

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.