Partial Regularity for Minimizers of Degenerate Polyconvex Energies

We prove partial regularity of minimizers for a class of polyconvex integral functionals $$\int_\Omega f (Du, \text{Ad}\, Du, \text{det}\, Du)\, dx,$$ where $f$ is degenerate convex. Our class includes the model case $$\int_\Omega (|Du|^p + |\text{Ad}\, Du|^p + |\text{det}\, Du|^p)\, dx.$$ The method of proof involves a blow-up technique combined with a suitable asymptotic analysis of the degeneration nature of the first term $\int_\Omega |Du|^p\, dx$.