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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
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506, U.S.A.

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
Copyright
Copyright © Royal Society of Edinburgh 1989

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