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Schauder Estimates for a Class of Potential Mean Field Games of Controls

Abstract : An existence result for a class of mean field games of controls is provided. In the considered model, the cost functional to be minimized by each agent involves a price depending at a given time on the controls of all agents and a congestion term. The existence of a classical solution is demonstrated with the Leray-Schauder theorem; the proof relies in particular on a priori bounds for the solution, which are obtained with the help of a potential formulation of the problem.
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https://hal.inria.fr/hal-02048437
Contributor : J. Frederic Bonnans <>
Submitted on : Monday, February 25, 2019 - 3:28:04 PM
Last modification on : Monday, August 10, 2020 - 3:46:03 PM
Long-term archiving on: : Sunday, May 26, 2019 - 3:01:11 PM

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Joseph Frédéric Bonnans, Saeed Hadikhanloo, Laurent Pfeiffer. Schauder Estimates for a Class of Potential Mean Field Games of Controls. Applied Mathematics and Optimization, Springer Verlag (Germany), 2019, pp.34. ⟨hal-02048437⟩

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