Examples of rank-one convex functions

Vladimír Šverák

doi:10.1017/S0308210500024410

Examples of rank-one convex functions

Vladimír Šverák

Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	237-242
Number of pages	6
Journal	Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Volume	114
Issue number	3-4
DOIs	https://doi.org/10.1017/S0308210500024410
State	Published - Jan 1 1990

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title = "Examples of rank-one convex functions",

abstract = "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.",

author = "Vladim{\'i}r {\v S}ver{\'a}k",

year = "1990",

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