An example of a C1,1 polyconvex function with no differentiable convex representative

We construct a C-1,C-1 polyconvex function W such that there exists a fixed 2 x 2 matrix Y with the property that all convex representatives of W have at least two distinct subgradients (and are hence not differentiable) at the point (Y, del Y), showing in particular that a polyconvex function can be smoother than any of its convex representatives. To cite this article: J. Bevan, C. R. Acad. Sci. Paris, Ser. I336 (2003). (C) 2003 Academie des sciences/Editions scientifiques et medicales Elsevier SAS. All rights reserved.