Abstract.
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.
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Received: 30 November 2001 / Accepted: 23 January 2002 / Published online: 5 September 2002
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ID="*" Supported in part by NSF Grant DMS-0070480 and by the Miller Institute for Basic Research in Science, UC Berkeley
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Evans, L. Some new PDE methods for weak KAM theory. Cal Var 17, 159–177 (2003). https://doi.org/10.1007/s00526-002-0164-y
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DOI: https://doi.org/10.1007/s00526-002-0164-y