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Quasiconvexity equals lamination convexity for isotropic sets of 2 × 2 matrices
Published/Copyright:
October 31, 2013
Abstract
Let K be a given compact set of real 2×2 matrices that is isotropic, meaning invariant under the left and right action of the special orthogonal group. Then we show that the quasiconvex hull of K coincides with the lamination convex hull of order 2. In particular, there is no difference between quasiconvexity, rank-one convexity and lamination convexity for K. This is a generalization of a known result for connected sets.
Funding source: DFG
Award Identifier / Grant number: FOR 797 under Mie 459/5-2
The author would like to acknowledge the very helpful discussions with Martin Kružík.
Received: 2012-5-16
Revised: 2013-6-21
Accepted: 2013-10-10
Published Online: 2013-10-31
Published in Print: 2015-1-1
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Bi-Sobolev homeomorphism with zero minors almost everywhere
- Fine properties of the subdifferential for a class of one-homogeneous functionals
- Quasiconvexity equals lamination convexity for isotropic sets of 2 × 2 matrices
- Regularity of minimizers of the area functional in metric spaces
- On the relaxation of variational integrals in metric Sobolev spaces
Articles in the same Issue
- Frontmatter
- Bi-Sobolev homeomorphism with zero minors almost everywhere
- Fine properties of the subdifferential for a class of one-homogeneous functionals
- Quasiconvexity equals lamination convexity for isotropic sets of 2 × 2 matrices
- Regularity of minimizers of the area functional in metric spaces
- On the relaxation of variational integrals in metric Sobolev spaces
