ON THE RELATIONSHIP BETWEEN RANK-(n − 1) CONVEXITY AND S-QUASICONVEXITY
نویسنده
چکیده
Abstract. We prove that rank-(n−1) convexity does not imply S-quasiconvexity (i.e., quasiconvexity with respect to divergence free fields) in M for m > n, by adapting the well-known Šverák’s counterexample [5] to the solenoidal setting. On the other hand, we also remark that rank-(n − 1) convexity and Squasiconvexity turn out to be equivalent in the space of n×n diagonal matrices. This follows by a generalization of Müller’s work [4].
منابع مشابه
Rank-.n 1/ convexity and quasiconvexity for divergence free fields
We prove that rank-.n 1/ convexity does not imply quasiconvexity with respect to divergence free fields (so-called S-quasiconvexity) in M n for m > n, by adapting the well-known Šverák’s counterexample 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.
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تاریخ انتشار 2009