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Aubry-Mather measures in the non convex setting

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journal contribution
posted on 2023-06-08, 14:56 authored by Filippo Cagnetti, D Gomes, H V Tran
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

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Publication status

  • Published

File Version

  • Published version

Journal

SIAM Journal on Mathematical Analysis

ISSN

0036-1410

Publisher

Society for Industrial and Applied Mathematics

Issue

6

Volume

43

Page range

2601-2629

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2013-05-15

First Open Access (FOA) Date

2013-05-15

First Compliant Deposit (FCD) Date

2013-05-15

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