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• W3087382435 abstract "According to a 2002 theorem by Cardaliaguet and Tahraoui, an isotropic, compact and connected subset of the group $operatorname{GL}^+(2)$ of invertible $2times2-,$matrices is rank-one convex if and only if it is polyconvex. In a 2005 Journal of Convex Analysis article by Alexander~Mielke, it has been conjectured that the equivalence of rank-one convexity and polyconvexity holds for isotropic functions on $operatorname{GL}^+(2)$ as well, provided their sublevel sets satisfy the corresponding requirements. We negatively answer this conjecture by giving an explicit example of a function $W:operatorname{GL}^+tomathbb{R}$ which is not polyconvex, but rank-one convex as well as isotropic with compact and connected sublevel sets." @default.
• W3087382435 created "2020-09-25" @default.
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• W3087382435 date "2020-09-21" @default.
• W3087382435 modified "2023-10-18" @default.
• W3087382435 title "A rank-one convex, non-polyconvex isotropic function on $operatorname{GL}^+(2)$ with compact connected sublevel sets" @default.
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• W3087382435 hasPublicationYear "2020" @default.
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