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Interfaces and Free Boundaries
Article . 2015 . Peer-reviewed
Data sources: Crossref
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https://dx.doi.org/10.48550/ar...
Article . 2014
License: arXiv Non-Exclusive Distribution
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https://dx.doi.org/10.20347/wi...
Other literature type . 2015
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Obstacle mean-field game problem

Authors: Diogo A. Gomes; Stefania Patrizi;

Obstacle mean-field game problem

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.

Countries
Germany, Saudi Arabia
Keywords

ddc:510, article, penalization method, 35J87, mean-field games -- obstacle problem -- penalization method, Mean-field games, Penalization method, 510, mean-field games, Obstacle problem, Mathematics - Analysis of PDEs, obstacle problem, FOS: Mathematics, 49L99, Analysis of PDEs (math.AP)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
22
Top 10%
Top 10%
Top 10%
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gold