Polyconvexity equals rank-one convexity for connected isotropic sets in \(\mathbb M^{2\times 2}\)

DOI10.1016/S1631-073X(03)00333-9zbMath1050.49010OpenAlexW2067088366MaRDI QIDQ1408922

Mario Romeo, Camillo De Lellis, Sergio Conti, Stefan Müller

Publication date: 26 September 2003

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s1631-073x(03)00333-9

zbMATH Keywords

integral functionalsquasiconvexitysingular values

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Inequalities and extremum problems involving convexity in convex geometry (52A40)

Related Items (3)

Automatic quasiconvexity of homogeneous isotropic rank-one convex integrands ⋮ A rank-one convex, nonpolyconvex isotropic function on with compact connected sublevel sets ⋮ On quasiconvex hulls in symmetric \(2\times 2\) matrices

Cites Work

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• Equivalence between rank-one convexity and polyconvexity for isotropic sets of \({\mathbb R}^{2{\times}2}\). I
• Equivalence between rank-one convexity and polyconvexity for isotropic sets of \({\mathbb R}^{2{\times}2}\). II
• Examples of rank-one convex functions
• Sur l'équivalence de la 1-rang convexité et de la polyconvexité des ensembles isotropiques de
• Rotationally invariant rank 1 convex functions

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