Quasiconvexity: the quadratic case revisited, and some consequences for fourth-degree polynomials

DOI10.1515/ACV.2010.023zbMath1216.49011MaRDI QIDQ2999539

Pablo Pedregal, Luis Bandeira

Publication date: 13 May 2011

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

zbMATH Keywords

quasiconvexityrank-one convexitysequential weak lower semicontinuity

Mathematics Subject Classification ID

Existence theories for free problems in two or more independent variables (49J10) Methods involving semicontinuity and convergence; relaxation (49J45)

Cites Work

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• Finding new families of rank-one convex polynomials
• \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
• An example of a quasiconvex function that is not polyconvex in two dimensions
• Convexity conditions and existence theorems in nonlinear elasticity
• Higher-order quasiconvexity reduces to quasiconvexity
• Die Darstellung biquadratischer Formen als Summen von Quadraten mit Anwendung auf die Variationsrechnung
• Quasiconvex functions can be approximated by quasiconvex polynomials
• Rank-one convexity implies quasi-convexity on certain hypersurfaces

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