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Journal of Convex Analysis 08 (2001), No. 1, 001--038
Copyright Heldermann Verlag 2001

Partial Regularity for Minimizers of Degenerate Polyconvex Energies

Luca Esposito
Dip. di Ingegneria dell'Informazione e Matematica Applicata, UniversitÓ di Salerno, Italy

Giuseppe Mingione
Dip. di Matematica, UniversitÓ di Parma, Via D'Azeglio 85/a, 43100 Parma, Italy


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

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