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

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 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...

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Veröffentlicht in:Advances in calculus of variations 2010-07, Vol.3 (3), p.279-285
1. Verfasser: Palombaro, Mariapia
Format: Artikel
Sprache:eng
Schlagworte:
lower semicontinuity
quasiconvexity
solenoidal fields
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Zusammenfassung: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.
ISSN:1864-8258
1864-8266
DOI:10.1515/acv.2010.010