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ESAIM: COCV, Vol. 13, N°4, pp. 692-706
DOI: 10.1051/cocv:2007033

Partial regularity for anisotropic functionals of higher order

Menita Carozza1 and Antonia Passarelli di Napoli2

1  Dipartimento Pe.Me.Is, Università degli studi del Sannio, Piazza Arechi 2, 82100 Benevento, Italy; carozza@unisannio.it
2  Dipartimento di Matematica e Applicazioni "R. Caccioppoli" Università di Napoli "Federico II", via Cintia, 80126 Napoli, Italy; antonia.passarelli@unina.it


(Received February 6, 2006. Revised June 8, 2006. Published online July 20, 2007.)

Abstract

We prove a $C^{k,\alpha}$ partial regularity result for local minimizers of variational integrals of the type $I(u)=\int_\Omega f(D^{k}u(x)){\rm d}x$, assuming that the integrand f satisfies (p,q) growth conditions.


Mathematics Subject Classification. 35G99, 49N60, 49N99

Key words: Partial regularity, non standard growth, higher order derivatives


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