Weak KAM Theorem in Lagrangian Dynamics

By A. Fathi. 2001

512 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/64745a5e7b9ba82fae8f9ce02753b498abfa13fc

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Citations in the corpus

Anosov magnetic flows, critical values and topological entropy (2002, background): “2 in [17] there exists a constant δ0 > 0 such that if x, y ∈ α([0, T ]) and δ ∈ [0, δ0] satisfy d(x, y) ≤ δ, then there exists a magnetic geodesic defined in [0, δ] that connects x to y and that minimizes the action among all absolutely continuous curves from the fixed interval [0, δ] into M̃ that c”
On smooth time functions (2011, methodology): “S´anchez contributions, and use instead some tools and results issued from weak KAM theory, see [8] for a comprehensive treatment of this topic.”
Viscosity Limit of Stationary Distributions for the Random Forced Burgers Equation (2005, background): “Such points of differentiability are exactly the uniqueness points for the backward and forward one-sided minimizer starting at time t at this point (see Fathi [4]).”
On Asymmetric Distances (2013, unknown): “If l < len(γ) and 0, 1 ∈ Sk , then we can assume moreover that ∃K,∀k > K,∀t, s ∈ Tk consecutive points20 len(ξk |[t,s]) ≤ len(γ|[t,s]) .”
Optimal mass transportation and Mather theory (2004, methodology): “We will not give proofs, and instead refer to [19], [20], [13], as well as the appendix in [7].”
Variational principle for contact Hamiltonian systems and its applications (2017, background): “Fathi [5, 6] generalized this result to equation (1.”
On the Hausdorff dimension of the mather quotient (2007, background): “Thus we obtain easily the first and the second equality.”
Existence of C1 critical subsolutions of the Hamilton-Jacobi equation (2004, methodology): “Moreover, see [4] or [9], we can apply Tonelli’s theorem to obtain Theorem 2.”
On the Homogenization of the Hamilton-Jacobi Equation (2019, methodology): “It is a classical result that the variational solution to (9) is given by the Lax–Oleinik formula (see for example [14, 15, 21] ):”
Burgers Turbulence (2007, methodology): “Mainly used in the past as a simple illustration of the notion of entropy (or viscosity) solution for conservation laws [83,95,85], the Burgers equation was related in the eighties to the theory of Hamiltonian systems developed by Kolmogorov [80], Arnold [2] andMoser [93] (KAM), through the introduc”