Regularity for Mean-Field Games Systems with Initial-Initial Boundary Conditions: The Subquadratic Case
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Permanent link to this recordhttp://hdl.handle.net/10754/668749
MetadataShow full item record
AbstractIn the present paper, we study forward-forward mean-field games with a power dependence on the measure and subquadratic Hamiltonians. These problems arise in the numerical approximation of stationary mean-field games. We prove the existence of smooth solutions under dimension and growth conditions for the Hamiltonian. To obtain the main result, we combine Sobolev regularity for solutions of the Hamilton-Jacobi equation (using Gagliardo-Nirenberg interpolation) with estimates of polynomial type for solutions of the Fokker-Planck equation.
CitationGomes, D. A., & Pimentel, E. A. (2015). Regularity for Mean-Field Games Systems with Initial-Initial Boundary Conditions: The Subquadratic Case. Dynamics, Games and Science, 291–304. doi:10.1007/978-3-319-16118-1_15
Conference/Event nameInternational Conference and Advanced School Planet Earth, DGS II