Some evidence in favor of Morrey's conjecture

Abstract

We provide further evidence to favor the fact that rank-one convexity does not imply quasiconvexity for two-component maps in dimension two. We provide an explicit family of maps parametrized by $\tau$, and argue that, for small $\tau$, they cannot be achievable by lamination. In this way, Morrey's conjecture might turn out to be correct in all cases.

arXiv commentIf has been shown (Sebestyén, G., Székelyhidi, L., Jr., Laminates supported on cubes, J. Convex Anal. 24 (2017), no. 4, 1217--1237) that the example in this preprint cannot give rise to a true counterexample to the fact that rank-one convexity does not imply quasiconvexity in the 2x2 case

Cited by in corpus (2)

• Rank-one convexity implies polyconvexity for isotropic, objective and isochoric elastic energies in the two-dimensional case
• Laminates supported on cubes