caa a22 4500 388108800 CHVBK 20180307125347.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500031085 doi S0308210500031085 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500031085 Šilhavý Miroslav Mathematical Institute of the AV ČR, Žitná 25, 115 67 Prague 1. Czech Republic On isotropic rank 1 convex functions [Elektronische Daten] [Miroslav Šilhavý] Let f be a rotationally invariant function defined on the set Lin+ of all tensors with positive determinant on a vector space of arbitrary dimension. Necessary and sufficient conditions are given for the rank 1 convexity of f in terms of its representation through the singular values. For the global rank 1 convexity on Lin+, the result is a generalization of a two-dimensional result of Aubert. Generally, the inequality on contains products of singular values of the type encountered in the definition of polyconvexity, but is weaker. It is also shown that the rank 1 convexity is equivalent to a restricted ordinary convexity when f is expressed in terms of signed invariants of the deformation. Copyright © Royal Society of Edinburgh 1999 Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/5(1999), 1081-1105 0308-2105 129:5<1081 1999 129 PRM https://doi.org/10.1017/S0308210500031085 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500031085 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Šilhavý Miroslav Mathematical Institute of the AV ČR, Žitná 25, 115 67 Prague 1. Czech Republic NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/5(1999), 1081-1105 0308-2105 129:5<1081 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge