Linear programming interpretations of Mather’s variational principle
L. C. Evans, D. Gomes (2002)
ESAIM: Control, Optimisation and Calculus of Variations
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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 -dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [6, 7, 8, 5].