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We provide an approximation of Mather variational problem by finite dimensional minimization problems in the framework of Γ-convergence. By a linear programming interpretation as done in [Evans and Gomes, ESAIM: COCV 8 (2002) 693-702] we state a duality theorem for the Mather problem, as well a finite dimensional approximation for the dual problem.
@article{COCV_2010__16_4_1094_0,
author = {Granieri, Luca},
title = {A finite dimensional linear programming approximation {of~Mather's} variational problem},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1094--1109},
publisher = {EDP-Sciences},
volume = {16},
number = {4},
year = {2010},
doi = {10.1051/cocv/2009039},
mrnumber = {2744164},
zbl = {1205.37077},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009039/}
}
TY - JOUR AU - Granieri, Luca TI - A finite dimensional linear programming approximation of Mather's variational problem JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 1094 EP - 1109 VL - 16 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009039/ DO - 10.1051/cocv/2009039 LA - en ID - COCV_2010__16_4_1094_0 ER -
%0 Journal Article %A Granieri, Luca %T A finite dimensional linear programming approximation of Mather's variational problem %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 1094-1109 %V 16 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009039/ %R 10.1051/cocv/2009039 %G en %F COCV_2010__16_4_1094_0
Granieri, Luca. A finite dimensional linear programming approximation of Mather's variational problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 1094-1109. doi: 10.1051/cocv/2009039
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