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MiS Preprint
50/2004

Rank-one convex functions on 2x2 symmetric matrices and laminates on rank-three lines

Sergio Conti, Daniel Faraco, Francesco Maggi and Stefan Müller

Abstract

We construct a function on the space of symmetric $2\times 2$ 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 $L^1$ 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.

Received:
Aug 13, 2004
Published:
Aug 13, 2004

Related publications

inJournal
2005 Repository Open Access
Sergio Conti, Daniel Faraco, Francesco Maggi and Stefan Müller

Rank-one convex functions on 2x2 symmetric matrices and laminates on rank-three lines

In: Calculus of variations and partial differential equations, 24 (2005) 4, pp. 479-493