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.

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.

DOI : 10.1051/cocv/2009039
Classification : 37J50, 49Q20, 49N60, 74P20, 65K10
Mots-clés : Mather problem, minimal measures, linear programming, Γ-convergence 
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     title = {A finite dimensional linear programming approximation {of~Mather's} variational problem},
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     pages = {1094--1109},
     publisher = {EDP-Sciences},
     volume = {16},
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     doi = {10.1051/cocv/2009039},
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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://www.numdam.org/articles/10.1051/cocv/2009039/

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