Preprint 19/1998

Quasiconvexity is not invariant under transposition

Stefan Müller

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Submission date: 18. Jun. 1998
Pages: 9
published in: Proceedings of the Royal Society of Edinburgh / A, 130 (2000) 2, p. 389-395 
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An example is given of a quasiconvex tex2html_wrap_inline44 such that the transposed function tex2html_wrap_inline46 given by tex2html_wrap_inline48 is not quasiconvex. For tex2html_wrap_inline50 one can take Sverák's quartic polynomial that is rank-one convex but not quasiconvex. The proof is closely related to the observation that the map tex2html_wrap_inline52 is weakly continuous from tex2html_wrap_inline54 into distributions provided that tex2html_wrap_inline56 is compact in tex2html_wrap_inline58.

23.06.2018, 02:10