Graber, P. Jameson and Mészáros, Alpár R. and Silva, Francisco J. and Tonon, Daniela (2019) 'The planning problem in mean field games as regularized mass transport.', Calculus of variations and partial differential equations., 58 (3). p. 115.
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.
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||https://doi.org/10.1007/s00526-019-1561-9|
|Publisher 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|
|Date accepted:||30 April 2019|
|Date deposited:||28 February 2020|
|Date of first online publication:||10 June 2019|
|Date first made open access:||10 June 2020|
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