Published Paper

Inserted: 17 aug 2004
Last Updated: 14 dec 2006

Journal: Calc. Var. Partial Differential Equations
Volume: 24
Number: 4
Pages: 479-493
Year: 2005
Notes:

Preprint MPI-MIS 502004

Abstract:

We construct a function on the space of 2x2 symmetric matrices in such a way that it is convex on rank-one directions and its distributional Hessian is not a locally bounded measure. This paper is also an illustration of a recently proposed technique to disprove L¹ estimates by the construction of suitable probability measures (laminates) in matrix space. From this point of view the novelty is that the support of the laminate, besides satisfying a convex constraint, needs to be contained on a rank-three line, up to arbitrarily small errors.

Keywords: bounded variation, convex integration, rank-one convexity, laminates