Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

S. Conti - C. De Lellis - S. Mueller - M. Romeo

Polyconvexity equals rank-one convexity for connected isotropic sets in $M^{2\times 2}$

created on 14 Nov 2002
modified by delellis on 03 May 2011


Published Paper

Inserted: 14 nov 2002
Last Updated: 3 may 2011

Journal: C. R. Math. Acad. Sci. Paris
Volume: 337
Number: 4
Pages: 233-238
Year: 2003


We give a short, self-contained argument showing that, for compact connected sets in $M^{2\times 2}$ which are invariant under the left and right action of SO(2), polyconvexity is equivalent to rank-one convexity (and even to lamination convexity). As a corollary, the same holds for O(2)-invariant compact sets. These results were first proved by Cardaliaguet and Tahraoui. We also give an example showing that the assumption of connectedness is necessary in the SO(2) case.

For the most updated version and eventual errata see the page


Credits | Cookie policy | HTML 4.0.1 strict | CSS 2.1