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

Hiroyoshi Mitake; Kohei Soga

doi:10.1007/s00526-018-1359-1

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

Hiroyoshi Mitake, Kohei Soga

Department of Mathematics

Research output: Contribution to journal › Article

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 language	English
Article number	78
Journal	Calculus of Variations and Partial Differential Equations
Volume	57
Issue number	3
DOIs	https://doi.org/10.1007/s00526-018-1359-1
Publication status	Published - 2018 Jun 1

Keywords

35B40
37J50
49L25

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s00526-018-1359-1

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Mitake, H., & Soga, K. (2018). Weak KAM theory for discounted Hamilton–Jacobi equations and its application. Calculus of Variations and Partial Differential Equations, 57(3), [78]. https://doi.org/10.1007/s00526-018-1359-1

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