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Tartar’s conjecture and localization of the quasiconvex hull in $ \mathbb{R}^{{2 \times 2}} $

Daniel Faraco Departamento de Matemáticas, Universidad Autónoma de Madrid László Székelyhidi Jr. Departement Mathematik, ETH Zürich

TBD mathscidoc:1701.331995

Acta Mathematica, 200, (2), 279-305, 2006.9
We give a concrete and surprisingly simple characterization of compact sets $ K \subset \mathbb{R}^{{2 \times 2}} $ for which families of approximate solutions to the inclusion problem$Du$∈$K$are compact. In particular our condition is algebraic and can be tested algorithmically. We also prove that the quasiconvex hull of compact sets of 2 × 2 matrices can be localized. This is false for compact sets in higher dimensions in general.
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@inproceedings{daniel2006tartar’s,
  title={Tartar’s conjecture and localization of the quasiconvex hull in $ \mathbb{R}^{{2 \times 2}} $ },
  author={Daniel Faraco, and László Székelyhidi Jr.},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203352092831704},
  booktitle={Acta Mathematica},
  volume={200},
  number={2},
  pages={279-305},
  year={2006},
}
Daniel Faraco, and László Székelyhidi Jr.. Tartar’s conjecture and localization of the quasiconvex hull in $ \mathbb{R}^{{2 \times 2}} $ . 2006. Vol. 200. In Acta Mathematica. pp.279-305. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203352092831704.
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