Rank-(n – 1) convexity and quasiconvexity for divergence free fields

DOI10.1515/ACV.2010.010zbMath1195.49022arXiv0904.4190MaRDI QIDQ3579834

Mariapia Palombaro

Publication date: 11 August 2010

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

Full work available at URL: https://arxiv.org/abs/0904.4190

zbMATH Keywords

lower semicontinuity\(\mathcal A\)-quasiconvexitysolenoidal fields

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45)

Related Items (4)

Shape optimization of light structures and the vanishing mass conjecture ⋮ On scaling properties for two-state problems and for a singularly perturbed \(T_3\) structure ⋮ Local invertibility in Sobolev spaces with applications to nematic elastomers and magnetoelasticity ⋮ Dimension reduction for functionals on solenoidal vector fields

Cites Work

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• Relaxation of three solenoidal wells and characterization of extremal three-phase \(H\)-measures
• Hydrodynamic structure of the augmented Born-Infeld equations
• Rigidity and lack of rigidity for solenoidal matrix fields
• Rank-one convexity implies quasi-convexity on certain hypersurfaces
• $\cal A$-Quasiconvexity, Lower Semicontinuity, and Young Measures

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