
Minimax Theory and its Applications 01 (2016), No. 1, 065082 Copyright Heldermann Verlag 2016 Local Regularity for MeanField Games in the Whole Space Diogo A. Gomes King Abdullah University of Science and Technology, CEMSE Division, Thuwal 239556900, Saudi Arabia diogo.gomes@kaust.edu.sa Edgard Pimentel Department of Mathematics, Universidade Federal de São Carlos, 13.560250 São CarlosSP, Brazil edgar@dm.ufscar.br [Abstractpdf] We investigate the Sobolev regularity for meanfield games in the whole space ${\mathbb R}^d$. This is achieved by combining integrability for the solutions of the FokkerPlanck equation with estimates for the HamiltonJacobi equation in Sobolev spaces. To avoid the mathematical challenges due to the lack of compactness, we prove an entropy dissipation estimate for the adjoint variable. This, together with the nonlinear adjoint method, yields uniform estimates for solutions of the HamiltonJacobi equation in $W^{1,p}_{loc}({\mathbb R}^d)$. [ Fulltextpdf (180 KB)] for subscribers only. 