Journal of Convex Analysis, Vol. 5, No. 1, pp. 107-117 (1998)

A Note on Quasiconvexity and Rank-one Convexity for 2$\times$2 Matrices

Pablo Pedregal and Vladimir Sverak

ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain, ppedrega@ind-cc.uclm.es, and School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA, sverak@math.umn.edu

Abstract: We report on an attempt to find a counterexample to the statement that rank-one convexity does not imply quasiconvexity in the case of 2$\times$2 matrices. The failure of such attempt is a consequence of some surprising computations.

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