An Aronsson type approach to extremal quasiconformal mappings

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:253

Article

Capogna, Luca^1,2  Raich, Andrew¹ 

[1] Univ Arkansas, Dept Math Sci, Fayetteville, AR 72701 USA

[2] Univ Minnesota, Inst Math & Applicat, Minneapolis, MN 55455 USA

关键词: Extremal quasiconformal mappings;    Quasiconformal mappings in R-n;    Flow of diffeomorphisms;    Trace dilation;   

DOI  :  10.1016/j.jde.2012.04.015

来源: Elsevier

【 摘 要 】

We study C-2 extremal quasiconformal mappings in space and establish necessary and sufficient conditions for a 'localized' form of extremality in the spirit of the work of G. Aronsson on absolutely minimizing Lipschitz extensions. We also prove short-time existence for smooth solutions of a gradient flow of QC diffeomorphisms associated to the extremal problem. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free