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Examples of rank-one convex functions

Published online by Cambridge University Press:  14 November 2011

Vladimír Šverák
Vladimír Šverák
Affiliation:
Katedra Matematické Analýzy, MFF-UK, Sokolovska 83, 18600 Prague 8, Czechoslovakia
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Synopsis

We construct rank-one convex functions which are not convex and have linear growth at infinity. We show that these functions could be useful in some problems concerning weak convergence of gradients if we were able to prove that they are quasiconvex. This question, however, seems to be open.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 3-4 , 1990 , pp. 237 - 242
Copyright
Copyright © Royal Society of Edinburgh 1990

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