Aubry-Mather measures in the non convex setting

Cagnetti, F, Gomes, D and Tran, H V (2011) Aubry-Mather measures in the non convex setting. SIAM Journal on Mathematical Analysis, 43 (6). pp. 2601-2629. ISSN 0036-1410

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Abstract

The adjoint method, introduced in [L. C. Evans, Arch. Ration. Mech. Anal., 197 (2010), pp. 1053–1088] and [H. V. Tran, Calc. Var. Partial Differential Equations, 41 (2011), pp. 301–319], is used to construct analogues to the Aubry–Mather measures for nonconvex Hamiltonians. More precisely, a general construction of probability measures, which in the convex setting agree with Mather measures, is provided. These measures may fail to be invariant under the Hamiltonian flow and a dissipation arises, which is described by a positive semidefinite matrix of Borel measures. However, in the case of uniformly quasiconvex Hamiltonians the dissipation vanishes, and as a consequence the invariance is guaranteed.

Copyright © 2011 Society for Industrial and Applied Mathematics

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Richard Chambers
Date Deposited: 15 May 2013 10:21
Last Modified: 09 Mar 2017 12:53
URI: http://sro.sussex.ac.uk/id/eprint/44716

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