Relaxation results for functions depending on polynomials changing sign on rank-one matrices

DOI10.1016/j.jmaa.2008.06.047zbMath1147.49011OpenAlexW2030060525MaRDI QIDQ953517

Omar Boussaid

Publication date: 6 November 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.06.047

zbMATH Keywords

calculus of variationsquasi-convexpolyconvex envelopespolynomial of several variablesrank-one convex

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Methods involving semicontinuity and convergence; relaxation (49J45)

Related Items (2)

Quasiconvexification of sets in optimal design ⋮ Inverse quasiconvexification

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
• Remarques sur les notions de polyconvexité, quasi-convexité et convexité de rang 1. (Remarks on polyconvexity, quasi-convexity and rank 1 convexity)
• An example of a quasiconvex function that is not polyconvex in two dimensions
• Convexity conditions and existence theorems in nonlinear elasticity
• On the different notions of convexity for rotationally invariant functions
• Quasi-convexity and the lower semicontinuity of multiple integrals
• Fully explicit quasiconvexification of the mean-square deviation of the gradient of the state in optimal design
• The extension of optimisation problems containing controls in the coefficients
• Explicit relaxation of a variational problem in optimal design
• Optimal design and relaxation of variational problems, I
• Rank-one convexity does not imply quasiconvexity
• The quasiconvex envelope of the Saint Venant–Kirchhoff stored energy function
• Direct methods in the calculus of variations

This page was built for publication: Relaxation results for functions depending on polynomials changing sign on rank-one matrices