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The planning problem in mean field games as regularized mass transport

Graber, P. Jameson; Mészáros, Alpár R.; Silva, Francisco J.; Tonon, Daniela

The planning problem in mean field games as regularized mass transport Thumbnail


Authors

P. Jameson Graber

Francisco J. Silva

Daniela Tonon



Abstract

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.

Citation

Graber, P. J., Mészáros, A. R., Silva, F. J., & Tonon, D. (2019). The planning problem in mean field games as regularized mass transport. Calculus of Variations and Partial Differential Equations, 58(3), Article 115. https://doi.org/10.1007/s00526-019-1561-9

Journal Article Type Article
Acceptance Date Apr 30, 2019
Online Publication Date Jun 10, 2019
Publication Date Jun 30, 2019
Deposit Date Oct 1, 2019
Publicly Available Date Mar 29, 2024
Journal Calculus of Variations and Partial Differential Equations
Print ISSN 0944-2669
Electronic ISSN 1432-0835
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 58
Issue 3
Article Number 115
DOI https://doi.org/10.1007/s00526-019-1561-9
Related Public URLs https://arxiv.org/abs/1811.02706

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Copyright Statement
This is a post-peer-review, pre-copyedit version of an article published in Calculus of variations and partial differential equations. The final authenticated version is available online at: https://doi.org/10.1007/s00526-019-1561-9





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