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The planning problem in mean field games as regularizedmass transport

Graber, Philip Jameson; Mészáros, Alpár Richárd; Silva, Francisco J.; Tonon, Daniela (2019), The planning problem in mean field games as regularizedmass transport, Calculus of Variations and Partial Differential Equations, 58, 3. 10.1007/s00526-019-1561-9

Type
Article accepté pour publication ou publié
Date
2019
Journal name
Calculus of Variations and Partial Differential Equations
Volume
58
Number
3
Publisher
Springer
Publication identifier
Metadata
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Author(s)
Graber, Philip Jameson

Mészáros, Alpár Richárd

Silva, Francisco J.

Tonon, Daniela
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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.
Subjects / Keywords
mean field games