Geodesic
Rank 1 convex hulls of isotropic functions in dimension 2 by 2
Mathematica Bohemica, Tome 126 (2001) no. 2, pp. 521-529.

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Let $f$ be a rotationally invariant (with respect to the proper orthogonal group) function defined on the set $\text{M}^{2\times 2}$ of all $2$ by $2$ matrices. Based on conditions for the rank 1 convexity of $f$ in terms of signed invariants of $\mathbb{A}$ (to be defined below), an iterative procedure is given for calculating the rank 1 convex hull of a rotationally invariant function. A special case in which the procedure terminates after the second step is determined and examples of the actual calculations are given.
DOI : 10.21136/MB.2001.134029
Classification : 49J45, 74G65, 74N99
Keywords: rank 1 convexity; relaxation; stored energies 
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     title = {Rank 1 convex hulls of isotropic functions in~dimension 2 by 2},
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Šilhavý, M. Rank 1 convex hulls of isotropic functions in dimension 2 by 2. Mathematica Bohemica, Tome 126 (2001) no. 2, pp. 521-529. doi : 10.21136/MB.2001.134029. http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.134029/

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