有限畸变的极值映射和Radon-Riesz性质

IF 1.3 2区数学 Q1 MATHEMATICS Revista Matematica Iberoamericana Pub Date : 2021-05-03 DOI:10.4171/rmi/1379

G. Martin, Cong Yao

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引用次数: 2

摘要

我们考虑平面域Ω⊂C之间的Sobolev映射f∈W（Ω，C），1本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Extremal mappings of finite distortion and the Radon–Riesz property

We consider Sobolev mappings f ∈ W (Ω,C), 1 < q < ∞, between planar domains Ω ⊂ C. We analyse the Radon-Riesz property for convex functionals of the form f 7→ ∫ Ω Φ(|Df(z)|, J(z, f)) dz and show that under certain criteria, which hold in important cases, weak convergence in W 1,q loc (Ω) of (for instance) a minimising sequence can be improved to strong convergence. This finds important applications in the minimisation problems for mappings of finite distortion and the L and Exp -Teichmüller theories.

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