Extremal mappings of finite distortion and the Radon-Riesz property (Q2692503)

Summary: We consider Sobolev mappings \(f \in W^{1, q}(\Omega, \mathbb{C})\), \(1 < q < \infty\), between planar domains \(\Omega \subset \mathbb{C}\). We analyse the Radon-Riesz property for polyconvex 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 \(W_{\mathrm{loc}}^{1, q} (\Omega)\) 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.