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Partial regularity of local minimizers of quasiconvex integrals with sub-quadratic growth

Published online by Cambridge University Press:  12 July 2007

Menita Carozza  and
Antonia Passarelli di Napoli
Menita Carozza
Affiliation:
Universitá del Sannio, Via dei Mulini, 82100 Benevento, Italy
Antonia Passarelli di Napoli
Affiliation:
Dipartimento di Matematica e Applicazioni, Universitá Monte S. Angelo, Via Cintia, 80126 Napoli, Italy
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Abstract

We prove partial regularity for local minimizers of quasiconvex integrals of the form I(v) = ∫ΩF(Dv(x))dx, where the integrand f(ξ) has sub-quadratic growth, i.e. |F(ξ)| ≤ L(1 + |ξ|p), with 1 < p < 2. A function u ∈ W1,p(Ω;RN) is a W1,q(Ω;RN) local minimizer of I(v) if there exists a δ > 0 such that I(u) ≤ I(v) whenever v and ‖Dv − Du‖q ≤ δ.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 6 , December 2003 , pp. 1249 - 1262
Copyright
Copyright © Royal Society of Edinburgh 2003

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