Abstract.
We extend the theory of Aubry-Mather measures to Hamiltonian systems that arise in vakonomic mechanics and sub-Riemannian geometry. We use these measures to study the asymptotic behavior of (vakonomic) action-minimizing curves, and prove a bootstrapping result to study the partial regularity of solutions of convex, but not strictly convex, Hamilton-Jacobi equations.
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Gomes, D.A. Hamilton-Jacobi methods for Vakonomic Mechanics. Nonlinear differ. equ. appl. 14, 233–257 (2007). https://doi.org/10.1007/s00030-007-5012-5
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DOI: https://doi.org/10.1007/s00030-007-5012-5