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.