Weak KAM theory for discounted Hamilton–Jacobi equations and its application

Hiroyoshi Mitake, Kohei Soga

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1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Article number78
JournalCalculus of Variations and Partial Differential Equations
Volume57
Issue number3
DOIs
Publication statusPublished - 2018 Jun 1

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Keywords

  • 35B40
  • 37J50
  • 49L25

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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