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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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:
06.07.06
Published:
06.07.06

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