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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.

Received:
Jul 6, 2006
Published:
Jul 6, 2006

Related publications

inJournal
2008 Repository Open Access
Daniel Faraco and László Székelyhidi

Tartar's conjecture and localization of the quasiconvex hull in \(\mathbb{R}^{2\times2}\)

In: Acta mathematica, 200 (2008) 2, pp. 279-305