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MiS Preprint
60/2006
Tartar's conjecture and localization of the quasiconvex hull in $\mathbb{R}^{2\times 2}$
Daniel Faraco and László Székelyhidi
Abstract
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 $Du\in K$ are compact. In particular our condition is algebraic and can be tested algorithmically. We also prove that the quasiconvex hull of compact sets of $2\times 2$ matrices can be localized. This is false for compact sets in higher dimensions in general.