Differential and Integral Equations

Uniqueness sets for minimization formulas

Yasuhiro Fujita and Hitosh Ishii

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012681

Mathematical Reviews number (MathSciNet)
MR2951743

Zentralblatt MATH identifier
1262.49033

Subjects
Primary: 54C40: Algebraic properties of function spaces [See also 46J10] 14E20: Coverings [See also 14H30] 46E25: Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15} 20C20: Modular representations and characters

Citation

Fujita, Yasuhiro; Ishii, Hitosh. Uniqueness sets for minimization formulas. Differential Integral Equations 25 (2012), no. 5/6, 579--588. https://projecteuclid.org/euclid.die/1356012681


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