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Weak KAM theory for discounted Hamilton-Jacobi equations and its application. (English) Zbl 1403.35083
Summary: Weak KAM theory for discounted Hamilton-Jacobi equations and corresponding discounted Lagrangian/Hamiltonian dynamics is developed. Then, it is applied to error estimates for viscosity solutions in the vanishing discount process. The main feature is to introduce and investigate the family of $$\alpha$$-limit points of minimizing curves, with some details in terms of minimizing measures. In error estimates, the family of $$\alpha$$-limit points is effectively exploited with properties of the corresponding dynamical systems.

##### MSC:
 35F21 Hamilton-Jacobi equations 35B40 Asymptotic behavior of solutions to PDEs 37J50 Action-minimizing orbits and measures (MSC2010) 49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games 37K55 Perturbations, KAM for infinite-dimensional Hamiltonian and Lagrangian systems 35D40 Viscosity solutions to PDEs
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