Acta Mathematica

, 200:279

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


DOI: 10.1007/s11511-008-0028-1

Cite this article as:
Faraco, D. & Székelyhidi, L. Acta Math (2008) 200: 279. doi:10.1007/s11511-008-0028-1


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.

Copyright information

© Institut Mittag-Leffler 2008

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad Autónoma de MadridMadridSpain
  2. 2.Departement MathematikETH ZürichZürichSwitzerland