Linear programming interpretations of Mather's variational principle
Department of Mathematics,
University of California,
Berkeley, CA 94720, USA; evans@math.Berkeley.EDU.
2 Department of Mathematics, University of Texas, Austin, TX 78712, USA.
Revised: 13 February 2002
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].
Mathematics Subject Classification: 90C05 / 35F20
Key words: Linear programming / duality / weak KAM theory.
© EDP Sciences, SMAI, 2002