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Journal Articles Applied Mathematics and Optimization Year : 2019

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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Dates and versions

hal-02048437 , version 1 (25-02-2019)

Identifiers

  • HAL Id : hal-02048437 , version 1

Cite

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