Two-dimensional examples of rank-one convex functions that are not quasiconvex

The aim of this note is to provide two-dimensional examples of rank-one convex functions which are not quasiconvex. 1. Introduction. In the study of equilibrium problems of nonlinear elasticity by the direct method of the calculus of variations the sequential weak lower semicontinuity (s.w.l.s.c.) of the functional of the total potential energy is required. The vector case involves integral functionals of the form J(u) = f x,u(x), ∇u(x))dx,