Abstract.
For convex superlinear lagrangians on a compact manifold M we characterize the Peierls barrier and the weak KAM solutions of the Hamilton-Jacobi equation, as defined by A. Fathi [9], in terms of their values at each static class and the action potential defined by R. Ma né [14]. When the manifold M is non-compact, we construct weak KAM solutions similarly to Busemann functions in riemannian geometry. We construct a compactification of \(M/_{d_c}\) by extending the Aubry set using these Busemann weak KAM solutions and characterize the set of weak KAM solutions using this extended Aubry set.
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Received: 13 November 2000 / Accepted: 4 December 2000 / Published online: 25 June 2001
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Contreras, G. Action potential and weak KAM solutions. Calc Var 13, 427–458 (2001). https://doi.org/10.1007/s005260100081
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DOI: https://doi.org/10.1007/s005260100081