An infinite-dimensional weak KAM theory via random variables

Diogo A. Gomes; Levon Nurbekyan

doi:10.3934/dcds.2016069

An infinite-dimensional weak KAM theory via random variables

Diogo A. Gomes, Levon Nurbekyan

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

2 Scopus citations

Abstract

We develop several aspects of the infinite-dimensional Weak KAM theory using a random variables' approach. We prove that the infinite-dimensional cell problem admits a viscosity solution that is a fixed point of the Lax-Oleinik semigroup. Furthermore, we show the existence of invariant minimizing measures and calibrated curves defined on R.

Original language	English (US)
Pages (from-to)	6167-6185
Number of pages	19
Journal	Discrete and Continuous Dynamical Systems
Volume	36
Issue number	11
DOIs	https://doi.org/10.3934/dcds.2016069
State	Published - Aug 31 2016

Access to Document

10.3934/dcds.2016069

Cite this

@article{b4c2853f77f74e0398f7244eb9fa1aaa,

title = "An infinite-dimensional weak KAM theory via random variables",

abstract = "We develop several aspects of the infinite-dimensional Weak KAM theory using a random variables' approach. We prove that the infinite-dimensional cell problem admits a viscosity solution that is a fixed point of the Lax-Oleinik semigroup. Furthermore, we show the existence of invariant minimizing measures and calibrated curves defined on R.",

author = "Gomes, {Diogo A.} and Levon Nurbekyan",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: The first author was partially supported by KAUST baseline and start-up funds and KAUST SRI, Center for Uncertainty Quanti cation in Computational Science and Engineering.",

year = "2016",

month = aug,

day = "31",

doi = "10.3934/dcds.2016069",

language = "English (US)",

volume = "36",

pages = "6167--6185",

journal = "Discrete and Continuous Dynamical Systems",

issn = "1078-0947",

publisher = "American Institute of Mathematical Sciences",

number = "11",

}

TY - JOUR

T1 - An infinite-dimensional weak KAM theory via random variables

AU - Gomes, Diogo A.

AU - Nurbekyan, Levon

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: The first author was partially supported by KAUST baseline and start-up funds and KAUST SRI, Center for Uncertainty Quanti cation in Computational Science and Engineering.

PY - 2016/8/31

Y1 - 2016/8/31

N2 - We develop several aspects of the infinite-dimensional Weak KAM theory using a random variables' approach. We prove that the infinite-dimensional cell problem admits a viscosity solution that is a fixed point of the Lax-Oleinik semigroup. Furthermore, we show the existence of invariant minimizing measures and calibrated curves defined on R.

AB - We develop several aspects of the infinite-dimensional Weak KAM theory using a random variables' approach. We prove that the infinite-dimensional cell problem admits a viscosity solution that is a fixed point of the Lax-Oleinik semigroup. Furthermore, we show the existence of invariant minimizing measures and calibrated curves defined on R.

UR - http://hdl.handle.net/10754/622516

UR - http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=12901

UR - http://www.scopus.com/inward/record.url?scp=84984910993&partnerID=8YFLogxK

U2 - 10.3934/dcds.2016069

DO - 10.3934/dcds.2016069

M3 - Article

SN - 1078-0947

VL - 36

SP - 6167

EP - 6185

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 11

ER -

An infinite-dimensional weak KAM theory via random variables

Abstract

Access to Document

Other files and links

Fingerprint

Cite this