Obstacle mean-field game problem

Handle URI:
http://hdl.handle.net/10754/594150
Title:
Obstacle mean-field game problem
Authors:
Gomes, Diogo A. ( 0000-0002-3129-3956 ) ; Patrizi, Stefania
Abstract:
In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions. © European Mathematical Society 2015.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
Citation:
Gomes D, Patrizi S (2015) Obstacle mean-field game problem. Interfaces and Free Boundaries 17: 55–68. Available: http://dx.doi.org/10.4171/ifb/333.
Publisher:
European Mathematical Publishing House
Journal:
Interfaces and Free Boundaries
Issue Date:
2015
DOI:
10.4171/ifb/333
Type:
Article
ISSN:
1463-9963
Sponsors:
KAUST, King Abdullah University of Science and Technology
Appears in Collections:
Articles; 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.date.accessioned2016-01-19T13:22:43Zen
dc.date.available2016-01-19T13:22:43Zen
dc.date.issued2015en
dc.identifier.citationGomes D, Patrizi S (2015) Obstacle mean-field game problem. Interfaces and Free Boundaries 17: 55–68. Available: http://dx.doi.org/10.4171/ifb/333.en
dc.identifier.issn1463-9963en
dc.identifier.doi10.4171/ifb/333en
dc.identifier.urihttp://hdl.handle.net/10754/594150en
dc.description.abstractIn this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions. © European Mathematical Society 2015.en
dc.description.sponsorshipKAUST, King Abdullah University of Science and Technologyen
dc.publisherEuropean Mathematical Publishing Houseen
dc.subjectMean-field gamesen
dc.subjectObstacle problemen
dc.subjectPenalization methoden
dc.titleObstacle mean-field game problemen
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.identifier.journalInterfaces and Free Boundariesen
dc.contributor.institutionWeierstrass Institute for Applied Analysis and Stochastics, Germanyen
kaust.authorGomes, Diogo A.en
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