Skip to main content Accessibility help
×
Home

A Caccioppoli inequality and partial regularity in the calculus of variations

  • Ronald F. Gariepy (a1)

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.

Copyright

References

Hide All
1Acerbi, E. and Fusco, N.. Semicontinuity problems in the calculus of variations. Arch.Rational Mech. Anal. 86 (1984), 125145.
2Acerbi, E. and Fusco, N.. A regularity theorem for minimizers of quasiconvex integrals. Arch. Rational Mech. Anal. 99 (1987), 261281.
3Evans, L. C.. Quasiconvexity and partial regularity in the calculus of variations. Arch. Rational Mech. Anal. 95 (1986), 227252.
4Evans, L. C. and Gariepy, R.. Blow-up, compactness, and partial regularity in the calculus of variations. Indiana Univ. Math. J. 36 (1987), 361371.
5Fusco, N. and Hutchinson, J.. C 1,α partial regularity of functions minimising quasiconvex integrals. Manuscripta Math. 4 (1985), 121143.
6Giaquinta, M.. Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Annals of Mathematics Studies (Princeton, NJ: Princeton University Press, 1983).
7Giaquinta, M.. Quasiconvexity, growth conditions, and partial regularity (preprint, 1987).
8Giaquinta, M. and Giusti, E.. Nonlinear elliptic systems with quadratic growth. Manuscripta Math. 24 (1978), 323349.
9Giusti, E. and Miranda, M.. Sulla regolarita delle soluzioni deboli di una classe di sistemi ellittici quasi-lineari. Arch. Rational Mech. Anal. 31 (1968), 173184.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed