An example of a quasiconvex function that is not polyconvex in two dimensions |
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| Authors: | Jean -Jacques Alibert Bernard Dacorogna |
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| Institution: | (1) Laboratoire d'Analyse Numérique, Université Paul Sabatier, 31062 Toulouse, France;(2) Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland |
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| Abstract: | We study the different notions of convexity for the function f
 ( ) = ||2 (||2 – 2 det ) where   2×2, introduced by Dacorogna & Marcellini. We show that f
is convex, polyconvex, quasiconvex, rank-one convex, if and only if ¦¦ 2/3  2, 1, 1+ (for some >0), 2/3, respectively. |
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