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

2 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

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10.1016/j.jde.2019.09.022

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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",

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AU - Jin, Liang

AU - Wang, Lin

AU - Yan, Jun

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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

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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

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Keywords

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