### Abstract

We study a Hamilton-Jacobi equation in infinite dimensions arising in optimal control theory for problems involving both exit times and state-space constraints. The corresponding boundary conditions for the Hamilton-Jacobi equation, of mixed nature, have been derived and investigated in [19], [2], [5], and [15] in the finite-dimensional case. We obtain a uniqueness result for viscosity solutions of such a problem and then prove the existence of a solution by showing that the value function is continuous.

Original language | English (US) |
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Pages (from-to) | 197-220 |

Number of pages | 24 |

Journal | Applied Mathematics & Optimization |

Volume | 24 |

Issue number | 1 |

DOIs | |

State | Published - Jul 1 1991 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Control and Optimization
- Applied Mathematics

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## Cite this

Cannarsa, P., Gozzi, F., & Soner, H. M. (1991). A boundary-value problem for Hamilton-Jacobi equations in hilbert spaces.

*Applied Mathematics & Optimization*,*24*(1), 197-220. https://doi.org/10.1007/BF01447742