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Polyconvexity equals rank-one convexity for connected isotropic sets in M2×2

✍ Scribed by Sergio Conti; Camillo De Lellis; Stefan Müller; Mario Romeo

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 149 KB
Volume: 337
Category: Article
ISSN: 1631-073X
DOI: 10.1016/s1631-073x(03)00333-9

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We provide some new necessary and sufficient conditions for regular isotropic rank-one convex functions on M + = {2 x 2 matrices such that det M >~ 0}. It is well known that isotmpic functions W(M) can be written as W(M) = G(AI, ),2) where Ai are the singular values of M. One of these conditions al