On the different convex hulls of sets involving singular values

DOI10.1017/S0308210500027311zbMath0915.15024OpenAlexW2041777496MaRDI QIDQ4229275

Chiara Tanteri, Bernard Dacorogna

Publication date: 28 June 1999

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500027311

zbMATH Keywords

convex hullsingular valuesreal matricespolyconvex hullrank one convex hull

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Convex sets in topological linear spaces; Choquet theory (46A55) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (7)

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 ⋮ Solutions of vectorial Hamilton-Jacobi equations and minimizers of nonquasiconvex functionals ⋮ \(\mathcal{D}\)-solutions to the system of vectorial calculus of variations in \(L^\infty\) via the singular value problem ⋮ Implicit partial differential equations and the constraints of nonlinear elasticity. ⋮ Calculus of variations, implicit partial differential equations and microstructure ⋮ On the minimum problem for non-quasiconvex vectorial functionals

Cites Work

• Unnamed Item
• Convexity conditions and existence theorems in nonlinear elasticity
• Cauchy-Dirichlet problem for first order nonlinear systems
• Direct methods in the calculus of variations

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