Two approaches to minimax formula of the additive eigenvalue for quasiconvex Hamiltonians

Nakayasu, Atsushi

doi:10.48550/arxiv.1412.6735

2014

DOI: 10.48550/arxiv.1412.6735

|View full text |Cite

Preprint

Two approaches to minimax formula of the additive eigenvalue for quasiconvex Hamiltonians

Atsushi Nakayasu

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2017

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since H 1 is quasiconvex and even, we use the inf-max representation formula for H 1 (see [4,16,36]) to get that…”

mentioning

confidence: 99%

Min–max formulas and other properties of certain classes of nonconvex effective Hamiltonians

Qian

Tran

2017

Math. Ann.

View full text Add to dashboard Cite

This paper is the first attempt to systematically study properties of the effective Hamiltonian H arising in the periodic homogenization of some coercive but nonconvex Hamilton-Jacobi equations. Firstly, we introduce a new and robust decomposition method to obtain min-max formulas for a class of nonconvex H. Secondly, we analytically and numerically investigate other related interesting phenomena, such as "quasi-convexification" and breakdown of symmetry, of H from other typical nonconvex Hamiltonians. Finally, in the appendix, we show that our new method and those a priori formulas from the periodic setting can be used to obtain stochastic homogenization for same class of nonconvex Hamilton-Jacobi equations. Some conjectures and problems are also proposed.2010 Mathematics Subject Classification. 35B10 35B20 35B27 35D40 35F21 .

show abstract

“…Since H 1 is quasiconvex and even, we use the inf-max representation formula for H 1 (see [4,16,36]) to get that…”

mentioning

confidence: 99%

Min–max formulas and other properties of certain classes of nonconvex effective Hamiltonians

Qian

Tran

2017

Math. Ann.

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Two approaches to minimax formula of the additive eigenvalue for quasiconvex Hamiltonians

Cited by 1 publication

References 14 publications

Min–max formulas and other properties of certain classes of nonconvex effective Hamiltonians

Min–max formulas and other properties of certain classes of nonconvex effective Hamiltonians

Contact Info

Product

Resources

About