The div-curl lemma ``trente ans après: an extension and an application to the \(G\)-convergence of unbounded monotone operators
From MaRDI portal
Publication:1019133
DOI10.1016/j.matpur.2009.01.002zbMath1183.35012OpenAlexW2109155283WikidataQ124833980 ScholiaQ124833980MaRDI QIDQ1019133
François Murat, Marc Briane, Juan Casado-Díaz
Publication date: 28 May 2009
Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.matpur.2009.01.002
Monotone operators and generalizations (47H05) Nonlinear elliptic equations (35J60) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27)
Related Items
A new div-curl result. applications to the homogenization of elliptic systems and to the weak continuity of the Jacobian, On the homogenization of partial integro-differential-algebraic equations, On the compensated compactness principle, Homogenization with an oscillating drift: from \(L^2\)-bounded to unbounded drifts, 2D compactness results, and 3D nonlocal effects, Asymptotic behavior of the linear elasticity system with varying and unbounded coefficients in a thin beam, The div-curl lemma for sequences whose divergence and curl are compact in \(W^{-1,1}\), Incompressible inelasticity as an essential ingredient for the validity of the kinematic decomposition \(\mathbf{F} = \mathbf{F}^{\mathrm{e}} \mathbf{F}^{\mathrm{i}}\), \(\Gamma\)-convergence of equi-coercive nonlinear energies defined on vector-valued functions, with non-uniformly bounded coefficients, Localisation principle for one-scale H-measures, Fractional div-curl quantities and applications to nonlocal geometric equations, Limiting Bourgain-Brezis estimates for systems of linear differential equations: theme and variations, Two-scale \(\Gamma \)-convergence of integral functionals and its application to homogenisation of nonlinear high-contrast periodic composites, Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations, A Global div-curl-Lemma for Mixed Boundary Conditions in Weak Lipschitz Domains, Weak continuity and compactness for nonlinear partial differential equations, Zhikov's hydromechanical lemma on compensated compactness: its extension and application to generalized stationary Navier–Stokes equations, Kinematics of elasto-plasticity: validity and limits of applicability of \(\mathbf{F}=\mathbf{F}^{\mathrm{e}}\mathbf{F}^{\mathrm{p}}\) for general three-dimensional deformations, A global div-curl-lemma for mixed boundary conditions in weak Lipschitz domains and a corresponding generalized \(A_0^*\)-\(A_1\)-lemma in Hilbert spaces, High‐contrast homogenization of linear systems of partial differential equations, Matrix representation of a cross product and related curl-based differential operators in all space dimensions
Cites Work
- \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
- G-convergence of monotone operators
- Homogenization of monotone operators in divergence form with \(x\)-dependent multivalued graphs
- The concentration-compactness principle in the calculus of variations. The limit case. I
- The general theory of homogenization. A personalized introduction
- Convergence of approximate solutions to conservation laws
- On the optimality of certain Sobolev exponents for the weak continuity of determinants
- Convexity conditions and existence theorems in nonlinear elasticity
- On the convergence of solutions of degenerate elliptic equations in divergence form
- On Poincaré's and J. L. Lions' lemmas
- \({\mathcal H}^1\)-estimates of Jacobians by subdeterminants
- Compensated compactness and Hardy spaces
- Asymptotic behaviour of equicoercive diffusion energies in dimension two
- Distributional convergence of null Lagrangians under very mild conditions
- Weak convergence of completely additive vector functions on a set
- Weak continuity and lower semicontinuity results for determinants
- Boundary estimates for elliptic systems with \(L^{1}\)- data
- Two-Dimensional Div-Curl Results: Application to the Lack of Nonlocal Effects in Homogenization
- Direct methods in the calculus of variations
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
