Global-Local subadditive ergodic theorems and application to homogenization in elasticity
A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources
We show how to capture the gradient concentration of the solutions of Dirichlet-type problems subjected to large sources of order concentrated on an -neighborhood of a hypersurface of the domain. To this end we define the gradient Young-concentration measures generated by sequences of finite energy and establish a very simple characterization of these measures.
A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources
We show how to capture the gradient concentration of the solutions of Dirichlet-type problems subjected to large sources of order concentrated on an -neighborhood of a hypersurface of the domain. To this end we define the gradient Young-concentration measures generated by sequences of finite energy and establish a very simple characterization of these measures.
The nonlinear membrane model : a Young measure and varifold formulation
We establish two new formulations of the membrane problem by working in the space of -Young measures and -varifolds. The energy functional related to these formulations is obtained as a limit of the formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing sequences...
Homogenization of periodic nonconvex integral functionals in terms of Young measures
Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the -limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.
Homogenization of periodic nonconvex integral functionals in terms of Young measures
Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the -limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.
The nonlinear membrane model: a Young measure and varifold formulation
We establish two new formulations of the membrane problem by working in the space of -Young measures and -varifolds. The energy functional related to these formulations is obtained as a limit of the formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing sequences...
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