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].
We prove the existence of classical solutions to certain fully non-linear second order elliptic equations with large zeroth order coefficient. The principal tool is an estimate asserting that the -norm of the solution cannot lie in a certain interval of the positive real axis.
We discuss some implications of linear programming for Mather theory [13-15] 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 [5-8].
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