Minimizers for a double-well problem with affine boundary conditions
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Publication:4260300
DOI10.1017/S0308210500021454zbMath0958.49008OpenAlexW2161624597MaRDI QIDQ4260300
Veronique Lods, Grégoire Allaire
Publication date: 4 April 2001
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/s0308210500021454
Existence theories for free problems in two or more independent variables (49J10) Methods involving semicontinuity and convergence; relaxation (49J45) Optimization of shapes other than minimal surfaces (49Q10)
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Cites Work
- \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
- Homogenization and optimal bounds in linear elasticity
- Fine phase mixtures as minimizers of energy
- The relaxation of a double-well energy
- Contre-exemples pour divers problèmes ou le contrôle intervient dans les coefficients
- Microstructures minimizing the energy of a two-phase elastic composite in two space dimensions. I: The confocal ellipse construction
- Existence of minimizers for non-quasiconvex functionals arising in optimal design
- Existence of minimizers for non-quasiconvex integrals
- Bounds and extremal microstructures for two-component composites: a unified treatment based on the translation method
- Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion
- Optimal design and relaxation of variational problems, I
- Exact estimates of the conductivity of a binary mixture of isotropic materials
- Optimal Bounds and Microgeometries for Elastic Two-Phase Composites
- Optimal bounds on the effective behavior of a mixture of two well-ordered elastic materials
- On characterizing the set of possible effective tensors of composites: The variational method and the translation method
- On the Trace of Matrix Products
- Direct methods in the calculus of variations
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