Preprint 1/1999

On Conditions for Polyconvexity

Jan Kristensen

Contact the author: Please use for correspondence this email.
Submission date: 24. Jan. 1999
Pages: 8
published in: Proceedings of the American Mathematical Society, 128 (2000) 6, p. 1793-1797 
MSC-Numbers: 49J10, 49J45
Keywords and phrases: polyconvexity, quasiconvexity, rank-1 convexity
Download full preprint: PDF (272 kB), PS ziped (128 kB)

We give an example of a smooth function tex2html_wrap_inline37, which is not polyconvex and that has the property that its restriction to any ball tex2html_wrap_inline39 of radius one can be extended to a smooth polyconvex function tex2html_wrap_inline41. In particular, it implies that there exists no `local condition' which is necessary and sufficient for polyconvexity of functions tex2html_wrap_inline43, where n, tex2html_wrap_inline47. We also briefly discuss connections with quasiconvexity.

03.07.2017, 01:40