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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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