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The planning problem in mean field games as regularizedmass transport

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Date
2019
Dewey
Analyse
Sujet
mean field games
Journal issue
Calculus of Variations and Partial Differential Equations
Volume
58
Number
3
Publication date
2019
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00526-019-1561-9
URI
https://basepub.dauphine.fr/handle/123456789/19404
Collections
  • CEREMADE : Publications
Metadata
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Author
Graber, Philip Jameson
Mészáros, Alpár Richárd
Silva, Francisco J.
Tonon, Daniela
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
In this paper, using variational approaches, we investigate the first order planning problem arising in the theory of mean field games. We show the existence and uniqueness of weak solutions of the problem in the case of a large class of Hamiltonians with arbitrary superlinear order of growth at infinity and local coupling functions. We require the initial and final measures to be merely summable. At the same time [relying on the techniques developed recently in Graber and Mészáros (Ann Inst H Poincaré Anal Non Linéaire 35(6):1557–1576, 2018)], under stronger monotonicity and convexity conditions on the data, we obtain Sobolev estimates on the solutions of the planning problem both for space and time derivatives.

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