ON THE RELATIONSHIP BETWEEN RANK-(n − 1) CONVEXITY AND S-QUASICONVEXITY
Mariapia Palombaro, Mariapia Palombaro · 2007
Abstract. We prove that rank-(n−1) convexity does not imply S-quasiconvexity (i.e., quasiconvexity with respect to divergence free fields) in M m×n for m> n, by adapting the well-known ˇ Sverák’s counterexample [5] to the solenoidal setting. On the other hand, we also remark that rank-(n − 1) convexity and S-quasiconvexity turn out to be equivalent in the space of n × n diagonal matrices. This follows by a generalization of Müller’s work [4].