# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc: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.
@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.