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A regularity theorem for minimisers of quasiconvex integrals: the case 1 <p<2*

Published online by Cambridge University Press:  14 November 2011

Menita Carozza  and
Antonia Passarelli di Napoli
Menita Carozza
Affiliation:
Dipartimento di Matematica e Applicazioni ‘R. Caccioppoli’, Universitá ‘Federico II’, Via Cintia, 80126 Napoli, Italy e-mail: [email protected]
Antonia Passarelli di Napoli
Affiliation:
Dipartimento di Matematica e Applicazioni ‘R. Caccioppoli’, Universitá ‘Federico II’, Via Cintia, 80126 Napoli, Italy e-mail: [email protected]
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Abstract

We prove partial regularity for minimisers of quasiconvex integrals of the form ∫Ωf(Du(x))dx. More precisely, we consider an integrand f(ξ) having subquadratic growth, i.e. | f(ξ)|≦L(1+|ξ|p) with p < 2. The case of a general integrand depending also on x and u is also considered.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 6 , 1996 , pp. 1181 - 1199
Copyright
Copyright © Royal Society of Edinburgh 1996

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