## Differential and Integral Equations

### Uniqueness sets for minimization formulas

#### 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.

#### Article information

Source
Differential Integral Equations, Volume 25, Number 5/6 (2012), 579-588.

Dates
First available in Project Euclid: 20 December 2012