On the relationship between rank-(n-1) convexity and S-quasiconvexity
Contact the author: Please use for correspondence this email.
Submission date: 07. Nov. 2007
Keywords and phrases: a-quasiconvexity, quasiconvexity, lower semicontinuity
Download full preprint: PDF (119 kB)
We prove that rank-(n-1) convexity does not imply -quasiconvexity (i.e., quasiconvexity with respect to divergence free fields) in the space of matrices for m>n, by adapting the well-known Sverák's counterexample to the solenoidal setting. On the other hand, we also remark that rank-(n-1) convexity and -quasiconvexity turn out to be equivalent in the space of diagonal matrices. This follows by a generalization of Müller's work.