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Journal of Differential Equations

Volume 268, Issue 5, 15 February 2020, Pages 2012-2039
Journal of Differential Equations

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

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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.

MSC

37J50
35F21
35D40

Keywords

Weakly coupled systems
Implicit variational principle
Viscosity solutions
Lipschitz regularity

Cited by (0)

☆

The first author is supported by the NSF of China (Grant 11571166, 11901293) and Startup Foundation of Nanjing University of Science and Technology (AE89991/114). The second author is supported by the NSF of China (Grant 11631006, 11790273). The third author is supported by the NSF of China (Grant 11790273, 11631006).

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