TITLE

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

AUTHOR(S)
Conti, S.; Faraco, D.; Maggi, F.; Müller, S.
PUB. DATE
December 2005
SOURCE
Calculus of Variations & Partial Differential Equations;Dec2005, Vol. 24 Issue 4, p479
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We construct a function on the space of symmetric 2× 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.
ACCESSION #
19234912

 

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