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 α-limit points of minimizing curves, with some details in terms of minimizing measures. In error estimates, the family of α-limit points is effectively exploited with properties of the corresponding dynamical systems.
|ジャーナル||Calculus of Variations and Partial Differential Equations|
|出版ステータス||Published - 2018 6 1|
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