### 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 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Differential and Integral Equations*,

*25*(5-6), 579-588.

**Uniqueness sets for minimization formulas.** / Fujita, Yasuhiro; Ishii, Hitoshi.

Research output: Contribution to journal › Article

*Differential and Integral Equations*, vol. 25, no. 5-6, pp. 579-588.

}

TY - JOUR

T1 - Uniqueness sets for minimization formulas

AU - Fujita, Yasuhiro

AU - Ishii, Hitoshi

PY - 2012/5

Y1 - 2012/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84886522782&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84886522782&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84886522782

VL - 25

SP - 579

EP - 588

JO - Differential and Integral Equations

JF - Differential and Integral Equations

SN - 0893-4983

IS - 5-6

ER -