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Subjects
37-XX Dynamical systems and ergodic theory
37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
37J50 Action-minimizing orbits and measures

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Linear programming interpretations of Mather’s variational principle

L. C. Evans, D. Gomes (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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].

Linear programming interpretations of Mather's variational principle

L. C. Evans, D. Gomes (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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 n-dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [5-8].

Currently displaying 1 – 2 of 2

Page 1