Quasiconvexity: the quadratic case revisited, and some consequences for fourth-degree

Abstract

We provide an alternative proof (based on ideas of mathematical programming) for the well-known quadratic case for which quasiconvexity and rank-one convexity are equivalent. It does not make use of Plancherel formula. Some consequences and some ideas for the case of 4th degree homogeneous polynomials are explored.