Extremal mappings of finite distortion and the Radon-Riesz property

We consider Sobolev mappings $fin W^{1,q}(Omega,IC)$, $1<q<infty$, between planar domains $Omegasubset IC$. We analyse the Radon-Riesz property for convex functionals of the form [fmapsto 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 $Exp$,-Teichmuller theories.