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Licensed Unlicensed Requires Authentication Published by De Gruyter April 12, 2010

Rank-(n – 1) convexity and quasiconvexity for divergence free fields

Mariapia Palombaro
From the journal

Abstract

We prove that rank-(n – 1) convexity does not imply quasiconvexity with respect to divergence free fields (so-called S-quasiconvexity) in 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.

Received: 2009-06-22
Revised: 2010-02-04
Accepted: 2010-02-01
Published Online: 2010-04-12
Published in Print: 2010-July

© de Gruyter 2010

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