Open AccessAn O(n) invariant rank 1 convex function that is not polyconvex
Author(s) -
Miroslav Šilhavý
Publication year - 2002
Publication title -
theoretical and applied mechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.279
H-Index - 6
eISSN - 2406-0925
pISSN - 1450-5584
DOI - 10.2298/tam0229325s
Subject(s) - invariant (physics) , convex hull , rank (graph theory) , regular polygon , mathematics , function (biology) , combinatorics , convex combination , convex function , pure mathematics , convex optimization , geometry , evolutionary biology , mathematical physics , biology
An O(n) invariant nonnegative rank 1 convex function of linear growth is given that is not polyconvex. This answers a recent question [8, p. 182] and [5]. The polyconvex hull of the function is calculated explicitly if n = 2:
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