# Extremal mappings of finite distortion and the Radon-Riesz property

@inproceedings{Martin2021ExtremalMO, title={Extremal mappings of finite distortion and the Radon-Riesz property}, author={Gaven J. Martin and Cong Yao}, year={2021} }

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…

## One Citation

The Teichm\"uller problem for $L^p$-means of distortion

- Mathematics
- 2021

Teichmüller’s problem from 1944 is this: Given x ∈ [0, 1) find and describe the extremal quasiconformal map f : D → D, f |∂D = identity and f(0) = −x ≤ 0. We consider this problem in the setting of…

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