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 › peer-review

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

Access to Document

10.1007/s00526-018-1359-1

Fingerprint Dive into the research topics of 'Weak KAM theory for discounted Hamilton–Jacobi equations and its application'. Together they form a unique fingerprint.

Cite this

@article{c00a05d0ee544404b9b17645a2dedaac,

title = "Weak KAM theory for discounted Hamilton–Jacobi equations and its application",

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.",

keywords = "35B40, 37J50, 49L25",

author = "Hiroyoshi Mitake and Kohei Soga",

year = "2018",

month = jun,

day = "1",

doi = "10.1007/s00526-018-1359-1",

language = "English",

volume = "57",

journal = "Calculus of Variations and Partial Differential Equations",

issn = "0944-2669",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Weak KAM theory for discounted Hamilton–Jacobi equations and its application

AU - Mitake, Hiroyoshi

AU - Soga, Kohei

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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.

AB - 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.

KW - 35B40

KW - 37J50

KW - 49L25

UR - http://www.scopus.com/inward/record.url?scp=85046106274&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85046106274&partnerID=8YFLogxK

U2 - 10.1007/s00526-018-1359-1

DO - 10.1007/s00526-018-1359-1

M3 - Article

AN - SCOPUS:85046106274

VL - 57

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

SN - 0944-2669

IS - 3

M1 - 78

ER -