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weak kam theory.

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Linear programming interpretations of Mather's variational principle
L. C. Evans, D. Gomes
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 8 / 2002

Published online by Cambridge University Press:

15 August 2002, pp. 693-702

Print publication:

2002
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We discuss some implications of linear programming for Mather theory [13-15] and itsfinite dimensional approximations. We find that the complementaryslackness condition of duality theory formally implies that the Mather set lies in ann-dimensional graph and as well predicts the relevant nonlinear PDE for the “weakKAM” theory of Fathi [5-8].