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2008 Tartar’s conjecture and localization of the quasiconvex hull in $ \mathbb{R}^{{2 \times 2}} $
Daniel Faraco, László Székelyhidi
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Acta Math. 200(2): 279-305 (2008). DOI: 10.1007/s11511-008-0028-1

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 DuK 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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Daniel Faraco. László Székelyhidi. "Tartar’s conjecture and localization of the quasiconvex hull in $ \mathbb{R}^{{2 \times 2}} $." Acta Math. 200 (2) 279 - 305, 2008. https://doi.org/10.1007/s11511-008-0028-1

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Received: 20 September 2006; Published: 2008
First available in Project Euclid: 31 January 2017

zbMATH: 1357.49054
MathSciNet: MR2413136
Digital Object Identifier: 10.1007/s11511-008-0028-1

Rights: 2008 © Institut Mittag-Leffler

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Vol.200 • No. 2 • 2008
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