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On convex representatives of polyconvex functions

Published online by Cambridge University Press:  12 July 2007

Jonathan Bevan
Jonathan Bevan
Affiliation:
Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, UK
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Abstract

The properties of convex representatives of polyconvex functions W : R2×2 → R are studied. The structure of the largest convex representative ϕW : R5 → R is given, and this is used to derive a representation formula for ϕW when W is C1 and satisfies a mild growth condition. The regularity of ϕW is discussed when W is C1; in particular, when W is C1, grows super-quadratically and is strictly polyconvex, it is shown that W has a C1 convex representative.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 1 , February 2006 , pp. 23 - 51
Copyright
Copyright © Royal Society of Edinburgh 2006

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