Conti, S; De Lellis, C; Müller, S; Romeo, M (2003). Polyconvexity equals rank-one convexity for connected isotropic sets in M2×2. Comptes Rendus Mathématique. Académie des Sciences. Paris, 337(4):233-238.
We give a short, self-contained argument showing that, for compact connected sets in M2x2 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.
We give a short, self-contained argument showing that, for compact connected sets in M2x2 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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics |
| Uncontrolled Keywords: | quasiconvexity, singular values, integral functionals |
| Language: | English |
| Date: | 2003 |
| Deposited On: | 17 Sep 2010 09:29 |
| Last Modified: | 25 Feb 2020 12:45 |
| Publisher: | Elsevier |
| ISSN: | 1631-073X |
| Additional Information: | English, French summary |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1016/S1631-073X(03)00333-9 |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=2009113 http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1050.49010 |
Conti, S