Some new PDE methods for weak KAM theory
- Cite this article as:
- Evans, L. Cal Var (2003) 17: 159. doi:10.1007/s00526-002-0164-y
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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.