On Conditions for Polyconvexity

Jan Kristensen

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Submission date: 24. Jan. 1999
Pages: 8
published in: Proceedings of the American Mathematical Society, 128 (2000) 6, p. 1793-1797 
DOI number (of the published article): 10.1090/S0002-9939-99-05387-3
Bibtex
MSC-Numbers: 49J10, 49J45
Keywords and phrases: polyconvexity, quasiconvexity, rank-1 convexity
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Abstract:
We give an example of a smooth function , which is not polyconvex and that has the property that its restriction to any ball of radius one can be extended to a smooth polyconvex function . In particular, it implies that there exists no `local condition' which is necessary and sufficient for polyconvexity of functions , where n, . We also briefly discuss connections with quasiconvexity.