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.
Mots-clés : Mather problem, minimal measures, linear programming, Γ-convergence
@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://archive.numdam.org/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://archive.numdam.org/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://archive.numdam.org/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. http://archive.numdam.org/articles/10.1051/cocv/2009039/
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