A new div-curl result. applications to the homogenization of elliptic systems and to the weak continuity of the Jacobian
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Publication:2634199
DOI10.1016/j.jde.2015.12.029zbMath1336.35045arXiv1501.02152OpenAlexW1821685582MaRDI QIDQ2634199
Publication date: 8 February 2016
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1501.02152
Effective constitutive equations in solid mechanics (74Q15) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Second-order elliptic systems (35J47)
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Cites Work
- The div-curl lemma for sequences whose divergence and curl are compact in \(W^{-1,1}\)
- The Jacobian determinant revisited
- Espaces de Dirichlet. I: Le cas élémentaire
- \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
- An introduction to Sobolev spaces and interpolation spaces
- New estimates for elliptic equations and Hodge type systems
- The div-curl lemma ``trente ans après: an extension and an application to the \(G\)-convergence of unbounded monotone operators
- The general theory of homogenization. A personalized introduction
- Compact sets in the space \(L^ p(0,T;B)\)
- Some properties of Gamma-limits of integral functionals
- On the optimality of certain Sobolev exponents for the weak continuity of determinants
- On the integrability of the Jacobian under minimal hypotheses
- Convexity conditions and existence theorems in nonlinear elasticity
- Composite media and asymptotic Dirichlet forms
- Weakly monotone functions
- An introduction to \(\Gamma\)-convergence
- A second gradient material resulting from the homogenization of an heterogeneous linear elastic medium
- Determination of the closure of the set of elasticity functionals
- Compensated compactness and Hardy spaces
- Asymptotic behaviour of equicoercive diffusion energies in dimension two
- Homogenization of convex functionals which are weakly coercive and not equi-bounded from above
- Homogenization of two-dimensional elasticity problems with very stiff coefficients
- Nonlocal effects in two-dimensional conductivity
- On the stability of conformal mappings in multidimensional spaces
- Weak continuity and lower semicontinuity results for determinants
- Homogenization of systems with equi-integrable coefficients
- Homogenization of non-uniformly bounded periodic diffusion energies in dimension two
- Homogenisation of a class of fourth order equations with application to incompressible elasticity
- CLOSURE OF THE SET OF DIFFUSION FUNCTIONALS WITH RESPECT TO THE MOSCO-CONVERGENCE
- Two-Dimensional Div-Curl Results: Application to the Lack of Nonlocal Effects in Homogenization
- Direct methods in the calculus of variations
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