Uniqueness sets for minimization formulas

Yasuhiro Fujita; Hitoshi Ishii

Uniqueness sets for minimization formulas

Yasuhiro Fujita, Hitoshi Ishii

Research output: Contribution to journal › Article › peer-review

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
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

Fingerprint Dive into the research topics of 'Uniqueness sets for minimization formulas'. Together they form a unique fingerprint.

Cite this

@article{c6f31c217a964051a24c3eedc1d5dc26,

title = "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.",

author = "Yasuhiro Fujita and Hitoshi Ishii",

year = "2012",

month = may,

language = "English",

volume = "25",

pages = "579--588",

journal = "Differential and Integral Equations",

issn = "0893-4983",

publisher = "Khayyam Publishing, Inc.",

number = "5-6",

}

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 -