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

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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.

源语言英语
页（从-至）2012-2039
页数28
期刊Journal of Differential Equations
卷268
期5
DOI
出版状态已出版 - 15 2月 2020
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Jin, L., Wang, L., & Yan, J. (2020). A representation formula of viscosity solutions to weakly coupled systems of Hamilton-Jacobi equations with applications to regularizing effect. Journal of Differential Equations, 268(5), 2012-2039. https://doi.org/10.1016/j.jde.2019.09.022