On the relationship between rank-(n-1) convexity and S-quasiconvexity

Mariapia Palombaro

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Submission date: 07. Nov. 2007
Pages: 7
MSC-Numbers: 49J45
Keywords and phrases: a-quasiconvexity, quasiconvexity, lower semicontinuity
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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.