We discuss some implications of linear programming for Mather theory [13, 14, 15] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an $n$-dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [6, 7, 8, 5].

Classification: 90C05, 35F20

Keywords: linear programming, duality, weak KAM theory

@article{COCV_2002__8__693_0, author = {Evans, L. C. and Gomes, D.}, title = {Linear programming interpretations of Mather's variational principle}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {8}, year = {2002}, pages = {693-702}, doi = {10.1051/cocv:2002030}, zbl = {1090.90143}, language = {en}, url = {http://www.numdam.org/item/COCV_2002__8__693_0} }

Evans, L. C.; Gomes, D. Linear programming interpretations of Mather's variational principle. ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002) pp. 693-702. doi : 10.1051/cocv:2002030. http://www.numdam.org/item/COCV_2002__8__693_0/

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