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A Caccioppoli inequality and partial regularity in the calculus of variations

Published online by Cambridge University Press:  14 November 2011

Ronald F. Gariepy
Ronald F. Gariepy
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506, U.S.A.
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Synopsis

A new proof is given of the partial regularity of minimisers under the principal assumptions of uniform strict quasiconvexity and polynomial growth. The proof is based on a Caccioppoli inequality and an “indirect” blow-up argument; this avoids the technical complications of a “direct” argument.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 112 , Issue 3-4 , 1989 , pp. 249 - 255
Copyright
Copyright © Royal Society of Edinburgh 1989

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References

1Acerbi, E. and Fusco, N.. Semicontinuity problems in the calculus of variations. Arch.Rational Mech. Anal. 86 (1984), 125–145.CrossRefGoogle Scholar
2Acerbi, E. and Fusco, N.. A regularity theorem for minimizers of quasiconvex integrals. Arch. Rational Mech. Anal. 99 (1987), 261–281.CrossRefGoogle Scholar
3Evans, L. C.. Quasiconvexity and partial regularity in the calculus of variations. Arch. Rational Mech. Anal. 95 (1986), 227–252.CrossRefGoogle Scholar
4Evans, L. C. and Gariepy, R.. Blow-up, compactness, and partial regularity in the calculus of variations. Indiana Univ. Math. J. 36 (1987), 361–371.CrossRefGoogle Scholar
5Fusco, N. and Hutchinson, J.. C 1,α partial regularity of functions minimising quasiconvex integrals. Manuscripta Math. 4 (1985), 121–143.CrossRefGoogle Scholar
6Giaquinta, M.. Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Annals of Mathematics Studies (Princeton, NJ: Princeton University Press, 1983).Google Scholar
7Giaquinta, M.. Quasiconvexity, growth conditions, and partial regularity (preprint, 1987).CrossRefGoogle Scholar
8Giaquinta, M. and Giusti, E.. Nonlinear elliptic systems with quadratic growth. Manuscripta Math. 24 (1978), 323–349.CrossRefGoogle Scholar
9Giusti, E. and Miranda, M.. Sulla regolarita delle soluzioni deboli di una classe di sistemi ellittici quasi-lineari. Arch. Rational Mech. Anal. 31 (1968), 173–184.CrossRefGoogle Scholar