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

被引：3

作者：

Jin, Liang ^{[1
]}

Wang, Lin ^{[2
]}

Yan, Jun ^{[3
]}

机构：

[1] Nanjing Univ Sci & Technol, Dept Appl Math, Nanjing 210094, Jiangsu, Peoples R China

[2] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

[3] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 268卷 / 05期

关键词：

Weakly coupled systems; Implicit variational principle; Viscosity solutions; Lipschitz regularity; LARGE-TIME BEHAVIOR; VANISHING CONTACT STRUCTURE;

D O I：

10.1016/j.jde.2019.09.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：2012 / 2039

页数：28

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