### Abstract

We establish general representation formulas for solutions of Hamilton-Jacobi equations widi convex Hamiltonians. In order to treat representation formulas on general domains, we introduce a notion of ideal boundary similar to the Martin boundary [21] in potential theory. We apply such representation formulas to investigate maximal solutions, in certain classes of functions, of Hamilton-Jacobi equations. Part of the results in this paper has been announced in [22]. Indiana University Mathematics Journal

Original language | English |
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Pages (from-to) | 2159-2183 |

Number of pages | 25 |

Journal | Indiana University Mathematics Journal |

Volume | 56 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2007 |

### Keywords

- Aubry sets
- Hamilton-Jacobi equations
- Representation fotmula
- State constraint problem
- Weak KAM theory

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Ishii, H., & Mitake, H. (2007). Representation formulas for solutions of Hamilton-Jacobi equations with convex hamiltonians.

*Indiana University Mathematics Journal*,*56*(5), 2159-2183. https://doi.org/10.1512/iumj.2007.56.3048