Geodesic
The nonlinear membrane model : a Young measure and varifold formulation
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 3, pp. 449-472 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

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 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.

DOI : 10.1051/cocv:2005014
Classification : 74K15, 35B05, 49J45
Keywords: membrane, Young measures, varifolds 
@article{COCV_2005__11_3_449_0,
     author = {Leghmizi, Med Lamine and Licht, Christian and Michaille, G\'erard},
     title = {The nonlinear membrane model : a {Young} measure and varifold formulation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {449--472},
     year = {2005},
     publisher = {EDP-Sciences},
     volume = {11},
     number = {3},
     doi = {10.1051/cocv:2005014},
     mrnumber = {2148853},
     zbl = {1081.74027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2005014/}
}
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
PY  - 2005
SP  - 449
EP  - 472
VL  - 11
IS  - 3
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2005014/
DO  - 10.1051/cocv:2005014
LA  - en
ID  - COCV_2005__11_3_449_0
ER  - 
%0 Journal Article
%A Leghmizi, Med Lamine
%A Licht, Christian
%A Michaille, Gérard
%T The nonlinear membrane model : a Young measure and varifold formulation
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2005
%P 449-472
%V 11
%N 3
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2005014/
%R 10.1051/cocv:2005014
%G en
%F COCV_2005__11_3_449_0
Leghmizi, Med Lamine; Licht, Christian; Michaille, Gérard. The nonlinear membrane model : a Young measure and varifold formulation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 3, pp. 449-472. doi: 10.1051/cocv:2005014

Cité par Sources :