Weak KAM theory topics in the stationary ergodic setting

DOI10.1007/s00526-011-0436-5zbMath1271.37041arXiv0907.5334OpenAlexW2055590439MaRDI QIDQ425164

Andrea Davini, Antonio Siconolfi

Publication date: 7 June 2012

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.5334

zbMATH Keywords

Lax-type formularandom Aubry setstationary ergodic Hamiltonian

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Viscosity solutions to PDEs (35D40) Hamilton-Jacobi equations (35F21)

Related Items (9)

Homogenization of the G-equation: a metric approach ⋮ Calibrated configurations for Frenkel-Kontorova type models in almost periodic environments ⋮ Metric techniques for convex stationary ergodic Hamiltonians ⋮ Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations ⋮ Homogenization of a class of one-dimensional nonconvex viscous Hamilton-Jacobi equations with random potential ⋮ Existence and regularity of strict critical subsolutions in the stationary ergodic setting ⋮ Stochastic homogenization of a nonconvex Hamilton-Jacobi equation ⋮ Stochastic homogenization of deterministic control problems ⋮ Stochastic homogenization of Hamilton-Jacobi equations on a junction

Cites Work

• Metric techniques for convex stationary ergodic Hamiltonians
• Exact and approximate correctors for stochastic Hamiltonians: The 1-dimensional case
• Multiscale Young measures in almost periodic homogenization and applications
• Viscosity solutions of Hamilton-Jacobi equations
• Ergodic problem for the Hamilton-Jacobi-Bellman equation. II
• Homogenization for stochastic Hamilton-Jacobi equations
• PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians
• A Generalized Dynamical Approach to the Large Time Behavior of Solutions of Hamilton--Jacobi Equations
• Bolza Problems with Discontinuous Lagrangians and Lipschitz-Continuity of the Value Function
• Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting
• Theory of Random Sets
• Convex Analysis
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
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