Calculus of Variations and Partial Differential Equations

, Volume 17, Issue 2, pp 159–177

Some new PDE methods for weak KAM theory

  • L.C. Evans

DOI: 10.1007/s00526-002-0164-y

Cite this article as:
Evans, L. Cal Var (2003) 17: 159. doi:10.1007/s00526-002-0164-y


We discuss a new approximate variational principle for weak KAM theory. The advantage of this approach is that we build both a minimizing measure and a solution of the generalized eikonal equation at the same time. Furthermore the approximations are smooth, and so we can derive some interesting formulas upon differentiating the Euler-Lagrange equation. Our method is inspired by the ”calculus of variations in the sup-norm” ideas of Aronsson, Jensen, Barron and others.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • L.C. Evans
    • 1
  1. 1.Department of Mathematics, University of California, Berkeley, CA 94720, USA US