We investigate the Sobolev regularity for mean-field games in the whole space Rd. This is achieved by combining integrability for the solutions of the Fokker-Planck equation with estimates for the Hamilton-Jacobi equation in Sobolev spaces. To avoid the mathematical chal- lenges due to the lack of compactness, we prove an entropy dissipation estimate for the adjoint variable. This, together with the non-linear adjoint method, yields uniform estimates for solutions of the Hamilton-Jacobi equation in Wloc1,p (Rd).
|Original language||English (US)|
|Number of pages||18|
|Journal||Minimax Theory and its Applications|
|State||Published - Jan 1 2016|
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics