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.
|Number of pages||10|
|Journal||Differential and Integral Equations|
|Publication status||Published - 2012 May|
ASJC Scopus subject areas
- Applied Mathematics