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Currently displaying 1 – 2 of 2

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The nonlinear membrane model : a Young measure and varifold formulation

Med Lamine Leghmizi; Christian Licht; Gérard Michaille — 2005

ESAIM: Control, Optimisation and Calculus of Variations

We establish two new formulations of the membrane problem by working in the space of $W_{Γ_{0}}^{1, p} (Ω, 𝐑^{3})$ -Young measures and $W_{Γ_{0}}^{1, p} (Ω, 𝐑^{3})$ -varifolds. The energy functional related to these formulations is obtained as a limit of the $3 d$ 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...

The nonlinear membrane model: a Young measure and varifold formulation

Med Lamine Leghmizi; Christian Licht; Gérard Michaille — 2010

ESAIM: Control, Optimisation and Calculus of Variations

We establish two new formulations of the membrane problem by working in the space of $W_{Γ_{0}}^{1, p} (Ω, 𝐑^{3})$ -Young measures and $W_{Γ_{0}}^{1, p} (Ω, 𝐑^{3})$ -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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