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Partial regularity for polyconvex functionals depending on the Hessian determinant

Authors:	Menita Carozza Chiara Leone Antonia Passarelli di Napoli Anna Verde

Institution:	(1) Dipartimento Pe.Me.Is, Università degli studi del Sannio, Piazza Arechi 2, 82100 Benevento, Italy;(2) Dipartimento di Matematica e Applicazioni “R.Caccioppoli”, Università di Napoli “Federico II”, Via Cintia, 80126 Napoli, Italy

Abstract:	We prove a C ^2,α partial regularity result for local minimizers of polyconvex variational integrals of the type ${I(u)=\int_\Omega \|D^{2}u\|^2+g({\det}(D^2u))dx}$ , where Ω is a bounded open subset of ${ \mathbb {R}^{2}}$ , ${u\in W_{loc}^{2,2}(\Omega)}$ and ${g\in C^{2}(\mathbb {R})}$ is a convex function, with subquadratic growth.

Keywords:	Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 35G99 49N60 49N99
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