### Abstract

A study on the Lax solution to a Hamilton-Jacobi equation is presented. It is proved that the function defined by the infimum-based Lax formula provides a solution almost everywhere in x for each fixed t>0 to the Hamilton-Jacobi, Cauchy problem. A generalization of the Lax formula is developed for the more inclusive Hamilton-Jacobi equation.

Original language | English (US) |
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Pages (from-to) | 629-640 |

Number of pages | 12 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 55 |

Issue number | 5 |

DOIs | |

State | Published - Nov 1 2003 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Keywords

- F set
- Hamilton-Jacobi equation
- Lax formula
- Lebesgue measure
- Semicontinuity
- Viscosity solution