Linear programming interpretations of Mather's variational principle

¹ 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.

Received: 10 October 2001
Revised: 13 February 2002

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].