PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians

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Selection problems for a discount degenerate viscous Hamilton–Jacobi equation (2017, methodology): “See [30, 29, 14, 15, 16, 7] for the study on the weak KAM theory and Mather measures.”
Exact and approximate correctors for stochastic Hamiltonians: the 1-dimensional case (2009, methodology): “Let us recall that such an object has been revealed to be useful, for H deterministic, in various contexts, see [6, 9, 12].”
Asymptotic Solutions of Hamilton-Jacobi Equations with State Constraints (2007, background): “See, for example, [12] or [17] for these properties.”
On smooth time functions (2011, methodology): “This is made through the introduction of an intrinsic length for curves which again only depends on the a–sublevels of the Hamiltonian, and, more precisely, on their support functions, see [7].”
Long-time Behavior of Solutions of Hamilton–Jacobi Equations with Convex and Coercive Hamiltonians (2009, background): “[13]) as the subset of R defined by AH = {y ∈ R | dH(·, y) ∈ SH}.”