English

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

Analysis of PDEs 2018-12-27 v2 Dynamical Systems

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.

Keywords

Cite

@article{arxiv.1707.02716,
  title  = {A representation formula of viscosity solutions to weakly coupled systems of Hamilton-Jacobi equations with applications to regularizing effect},
  author = {Liang Jin and Lin Wang and Jun Yan},
  journal= {arXiv preprint arXiv:1707.02716},
  year   = {2018}
}