Abstract
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) |
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Pages (from-to) | 65-82 |
Number of pages | 18 |
Journal | Minimax Theory and its Applications |
Volume | 1 |
Issue number | 1 |
State | Published - 2016 |
Bibliographical note
Publisher Copyright:© Heldermann Verlag.
ASJC Scopus subject areas
- Analysis
- Control and Optimization
- Computational Mathematics