# The nonlinear membrane model: a Young measure and varifold formulation

Med Lamine Leghmizi; Christian Licht; Gérard Michaille

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 11, Issue: 3, page 449-472
- ISSN: 1292-8119

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topLeghmizi, Med Lamine, Licht, Christian, and Michaille, Gérard. "The nonlinear membrane model: a Young measure and varifold formulation." ESAIM: Control, Optimisation and Calculus of Variations 11.3 (2010): 449-472. <http://eudml.org/doc/90772>.

@article{Leghmizi2010,

abstract = {
We establish two new formulations of the membrane problem by working in the space of $W^\{1,p\}_\{\Gamma_0\}(\Omega,\mathbf R^3)$-Young measures and $W^\{1,p\}_\{\Gamma_0\}(\Omega,\mathbf R^3)$-varifolds. The energy
functional related to these formulations is obtained as a limit of the 3d 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 related to the classical
formulation. The second formulation moreover
accounts for concentration effects.
},

author = {Leghmizi, Med Lamine, Licht, Christian, Michaille, Gérard},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Membrane; Young measures; varifolds.; energy functional; variational convergence},

language = {eng},

month = {3},

number = {3},

pages = {449-472},

publisher = {EDP Sciences},

title = {The nonlinear membrane model: a Young measure and varifold formulation},

url = {http://eudml.org/doc/90772},

volume = {11},

year = {2010},

}

TY - JOUR

AU - Leghmizi, Med Lamine

AU - Licht, Christian

AU - Michaille, Gérard

TI - The nonlinear membrane model: a Young measure and varifold formulation

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 11

IS - 3

SP - 449

EP - 472

AB -
We establish two new formulations of the membrane problem by working in the space of $W^{1,p}_{\Gamma_0}(\Omega,\mathbf R^3)$-Young measures and $W^{1,p}_{\Gamma_0}(\Omega,\mathbf R^3)$-varifolds. The energy
functional related to these formulations is obtained as a limit of the 3d 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 related to the classical
formulation. The second formulation moreover
accounts for concentration effects.

LA - eng

KW - Membrane; Young measures; varifolds.; energy functional; variational convergence

UR - http://eudml.org/doc/90772

ER -

## References

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