A representation formula of viscosity solutions to weakly coupled systems of Hamilton-Jacobi equations with applications to regularizing effect

Liang Jin; Lin Wang; Jun Yan

doi:10.1016/j.jde.2019.09.022

A representation formula of viscosity solutions to weakly coupled systems of Hamilton-Jacobi equations with applications to regularizing effect

Liang Jin
, Lin Wang
, Jun Yan

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Based on a fixed point argument, we give a dynamical representation of the viscosity solution to Cauchy problem of certain weakly coupled systems of Hamilton-Jacobi equations with continuous initial datum. Using this formula, we obtain some regularity results related to the viscosity solution, including a partial extension of Lions' regularizing effect [17] to the case of weakly coupled systems.

Original language	English
Pages (from-to)	2012-2039
Number of pages	28
Journal	Journal of Differential Equations
Volume	268
Issue number	5
DOIs	https://doi.org/10.1016/j.jde.2019.09.022
Publication status	Published - 15 Feb 2020
Externally published	Yes

Keywords

Implicit variational principle
Lipschitz regularity
Viscosity solutions
Weakly coupled systems

Access to Document

10.1016/j.jde.2019.09.022

Cite this

@article{cad9a7088c234398992337dbb3e6ace9,

title = "A representation formula of viscosity solutions to weakly coupled systems of Hamilton-Jacobi equations with applications to regularizing effect",

abstract = "Based on a fixed point argument, we give a dynamical representation of the viscosity solution to Cauchy problem of certain weakly coupled systems of Hamilton-Jacobi equations with continuous initial datum. Using this formula, we obtain some regularity results related to the viscosity solution, including a partial extension of Lions' regularizing effect [17] to the case of weakly coupled systems.",

keywords = "Implicit variational principle, Lipschitz regularity, Viscosity solutions, Weakly coupled systems",

author = "Liang Jin and Lin Wang and Jun Yan",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2020",

month = feb,

day = "15",

doi = "10.1016/j.jde.2019.09.022",

language = "English",

volume = "268",

pages = "2012--2039",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "5",

}

TY - JOUR

T1 - A representation formula of viscosity solutions to weakly coupled systems of Hamilton-Jacobi equations with applications to regularizing effect

AU - Jin, Liang

AU - Wang, Lin

AU - Yan, Jun

PY - 2020/2/15

Y1 - 2020/2/15

N2 - Based on a fixed point argument, we give a dynamical representation of the viscosity solution to Cauchy problem of certain weakly coupled systems of Hamilton-Jacobi equations with continuous initial datum. Using this formula, we obtain some regularity results related to the viscosity solution, including a partial extension of Lions' regularizing effect [17] to the case of weakly coupled systems.

AB - Based on a fixed point argument, we give a dynamical representation of the viscosity solution to Cauchy problem of certain weakly coupled systems of Hamilton-Jacobi equations with continuous initial datum. Using this formula, we obtain some regularity results related to the viscosity solution, including a partial extension of Lions' regularizing effect [17] to the case of weakly coupled systems.

KW - Implicit variational principle

KW - Lipschitz regularity

KW - Viscosity solutions

KW - Weakly coupled systems

UR - https://www.scopus.com/pages/publications/85072299454

U2 - 10.1016/j.jde.2019.09.022

DO - 10.1016/j.jde.2019.09.022

M3 - Article

AN - SCOPUS:85072299454

SN - 0022-0396

VL - 268

SP - 2012

EP - 2039

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 5

ER -

A representation formula of viscosity solutions to weakly coupled systems of Hamilton-Jacobi equations with applications to regularizing effect

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this