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Partial regularity of multiple variational integrals of any order

Published online by Cambridge University Press:  14 November 2011

Liu Xiangao
Affiliation:
Department of Mathematics, University of Hunan, Changsha Hunan, People's Republic of China

Synopsis

We prove Cm, μ almost everywhere regularity for minimisers of functional of the form ∫f(x, su, Dmu)dx, where f is uniformly strictly quasiconvex.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1990

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References

1Giaquinta, M. and Giusti, E.. Differentiability of minima of non-differentiable functionals. Invent. Math. 72 (1983), 285298.CrossRefGoogle Scholar
2Giaquinta, M.. Multiple integrals in the calculus of variations and nonlinear elliptic systems. (Princeton: Princeton University Press, 1983).Google Scholar
3Evans, L. C.. Quasiconvexity and partial regularity in the calculus of variations. Arch. Rational Mech. Anal. 95 (1986), 227252.CrossRefGoogle Scholar
4Fusco, N. and Hutchinson, J.. C1, α partial regularity of functions minimizing quasiconvex integrals. Manuscripta math. 54 (1985), 121143.CrossRefGoogle Scholar
5Aceroi, E. and Fusco, N.. A regularity theorem for minimizers of quasiconvex integrals. Arch. Rational Mech. Anal. 99 (1987), 261281.CrossRefGoogle Scholar
6Meyers, N. G.. Quasiconvexity and lower semicontinuity of multiple variational integrals of any order. Trans. Amer. Math. Soc. 119 (1965), 125149.CrossRefGoogle Scholar
7Min-Chun, Hong. Existence and partial regularity in the calculus of variations. Ann. Mat. Pura Appl. 149 (1987), 311328.CrossRefGoogle Scholar