Tartar’s conjecture and localization of the quasiconvex hull in ℝ2×2
Daniel Faraco and László Székelyhidi
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Submission date: 06. Jul. 2006
published in: Acta mathematica, 200 (2008) 2, p. 279-305
DOI number (of the published article): 10.1007/s11511-008-0028-1
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We give a concrete and surprisingly simple characterization of compact sets for which families of approximate solutions to the inclusion problem are compact. In particular our condition is algebraic and can be tested algorithmically. We also prove that the quasiconvex hull of compact sets of matrices can be localized. This is false for compact sets in higher dimensions in general.