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Linear programming interpretations of Mather's variational principle

Published online by Cambridge University Press:  15 August 2002

L. C. Evans  and
D. Gomes
L. C. Evans
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA; evans@math.Berkeley.EDU.
D. Gomes
Affiliation:
Department of Mathematics, University of Texas, Austin, TX 78712, USA.
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Abstract

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].

Keywords

Linear programmingdualityweak KAM theory.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 693 - 702
Copyright
© EDP Sciences, SMAI, 2002

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