On the existence of classical solutions for stationary extended mean field games

Handle URI:
http://hdl.handle.net/10754/563466
Title:
On the existence of classical solutions for stationary extended mean field games
Authors:
Gomes, Diogo A. ( 0000-0002-3129-3956 ) ; Patrizi, Stefania; Voskanyan, Vardan
Abstract:
In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish the existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in Lasry and Lions (2006), Gomes and Sanchez-Morgado (2011) or Gomes et al. (2012) this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where the existence of classical solutions can be proved. © 2013 Elsevier Ltd. All rights reserved.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ); Applied Mathematics and Computational Science Program
Publisher:
Elsevier BV
Journal:
Nonlinear Analysis: Theory, Methods & Applications
Issue Date:
Apr-2014
DOI:
10.1016/j.na.2013.12.016
ARXIV:
arXiv:1305.2696
Type:
Article
ISSN:
0362546X
Additional Links:
http://arxiv.org/abs/arXiv:1305.2696v1
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGomes, Diogo A.en
dc.contributor.authorPatrizi, Stefaniaen
dc.contributor.authorVoskanyan, Vardanen
dc.date.accessioned2015-08-03T11:52:13Zen
dc.date.available2015-08-03T11:52:13Zen
dc.date.issued2014-04en
dc.identifier.issn0362546Xen
dc.identifier.doi10.1016/j.na.2013.12.016en
dc.identifier.urihttp://hdl.handle.net/10754/563466en
dc.description.abstractIn this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish the existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in Lasry and Lions (2006), Gomes and Sanchez-Morgado (2011) or Gomes et al. (2012) this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where the existence of classical solutions can be proved. © 2013 Elsevier Ltd. All rights reserved.en
dc.publisherElsevier BVen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1305.2696v1en
dc.subjectA-priori estimatesen
dc.subjectClassical solutionsen
dc.subjectMean field gamesen
dc.titleOn the existence of classical solutions for stationary extended mean field gamesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)en
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalNonlinear Analysis: Theory, Methods & Applicationsen
dc.contributor.institutionCenter for Mathematical Analysis, Geometry and Dynamical Systems, Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugalen
dc.identifier.arxividarXiv:1305.2696en
kaust.authorGomes, Diogo A.en
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