A remark on the structure of the busemann representative of a polyconvex function

Bevan, JJ (2011) A remark on the structure of the busemann representative of a polyconvex function Journal of Convex Analysis, 18 (1). pp. 203-208.

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Abstract

Under mild conditions on a polyconvex function W : R → R, its largest convex representative, known as the Busemann representative, may be written as the supremum over all affine functions Φ : R →R satisfying Φ(ξ det ξ) ≤ W(ξ) for all 2 × 2 matrices ξ. In this paper, we construct an example of a polyconvex W : R → R whose Busemann representative is, on an open set, strictly larger than the supremum of all affine functions Φ as above and which also satisfy Φ(ξ , det ξ\ ) = W(ξ ) for at least one 2×2 matrix Ξ . © Heldermann Verlag.

Item Type:	Article
Divisions :	Faculty of Engineering and Physical Sciences > Mathematics
Authors :	Bevan, JJ
Date :	2011
Depositing User :	Symplectic Elements
Date Deposited :	28 Mar 2017 14:59
Last Modified :	10 Jun 2019 14:26
URI:	http://epubs.surrey.ac.uk/id/eprint/37253

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