Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Next Article Journal of Convex Analysis 08 (2001), No. 1, 001--038Copyright Heldermann Verlag 2001 Partial Regularity for Minimizers of Degenerate Polyconvex Energies Luca Esposito Dip. di Ingegneria dell'Informazione e Matematica Applicata, Università di Salerno, Italy Giuseppe Mingione Dip. di Matematica, Università di Parma, Via D'Azeglio 85/a, 43100 Parma, Italy [Abstract-pdf] 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 $\int_\Omega |Du|^p\, dx$. Keywords: Polyconvexity, regularity, elliptic systems. MSC: 49N60; 49N99, 35J20 [ Fulltext-pdf  (770  KB)]