Extremal mappings of finite distortion and the RadonRiesz property
Abstract
We consider Sobolev mappings $f\in W^{1,q}(\Omega,\IC)$, $1<q<\infty$, between planar domains $\Omega\subset \IC$. We analyse the RadonRiesz property for convex functionals of the form \[f\mapsto \int_\Omega \Phi(Df(z),J(z,f)) \; dz \] and show that under certain criteria, which hold in important cases, weak convergence in $W_{loc}^{1,q}(\Omega)$ 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 $L^p$ and $Exp$\,Teichmüller theories.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 arXiv:
 arXiv:2105.01222
 Bibcode:
 2021arXiv210501222M
 Keywords:

 Mathematics  Complex Variables;
 30C