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 -
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