### Abstract

In this paper, we consider minimization formulas which arise typically in optimal control and weak KAM theory for Hamilton Jacobi equations. Given a minimization formula, we define a uniqueness set for the formula, which replaces the original region of minimization without changing its values. Our goal is to provide a necessary and sufficient condition that a given set be a uniqueness set. We also provide a characterization of the existence of a minimal uniqueness set with respect to set inclusion.

Original language | English |
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Pages (from-to) | 579-588 |

Number of pages | 10 |

Journal | Differential and Integral Equations |

Volume | 25 |

Issue number | 5-6 |

Publication status | Published - 2012 May |

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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## Cite this

Fujita, Y., & Ishii, H. (2012). Uniqueness sets for minimization formulas.

*Differential and Integral Equations*,*25*(5-6), 579-588.