

Preprint 100/2007
On the relationship between rank-(n-1) convexity and S-quasiconvexity
Mariapia Palombaro
Contact the author: Please use for correspondence this email.
Submission date: 07. Nov. 2007
Pages: 7
MSC-Numbers: 49J45
Keywords and phrases: a-quasiconvexity, quasiconvexity, lower semicontinuity
Download full preprint: PDF (119 kB)
Abstract:
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.