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arXiv · 1707.02716

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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Abstract

Based on a fixed point argument, we give a {\it 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 \cite{L} to the case of weakly coupled systems.

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Liang Jin, Lin Wang, Jun Yan. 2017-07-10. A representation formula of viscosity solutions to weakly coupled systems of Hamilton-Jacobi equations with applications to regularizing effect. https://arxiv.org/abs/1707.02716

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