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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].

A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities

L. C. Evans; H. Ishii — 1985

Annales de l'I.H.P. Analyse non linéaire

Fully nonlinear second order elliptic equations with large zeroth order coefficient

L. C. Evans; Pierre-Louis Lions — 1981

Annales de l'institut Fourier

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 $C^{2, α}$ -norm of the solution cannot lie in a certain interval of the positive real axis.

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

A PDE approach to certain large deviation problems for systems of parabolic equations

L. C. Evans; P. E. Souganidis; G. Fournier; M. Willem — 1989

Annales de l'I.H.P. Analyse non linéaire

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