2023/11/17 by Yiming Jiang, Jingchuang Ren, Jiang, Yiming +5
Economics, Econometrics and Finance · Mathematics · #35A01 #35K65 #35Q89 #Analysis of PDEs (math.AP) #Climate Change Policy and Economics #FOS: Mathematics #Mathematical Biology Tumor Growth #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2311.10312
openalex publication_date 2023/11/17 · openalex created_date 2023/11/21 · openalex updated_date 2026/07/28
In this paper, we consider a class of infinitely degenerate partial differential systems to obtain the Nash equilibria in the mean field games. The degeneracy in the diffusion and the Hamiltonian may be different. This feature brings difficulties to the uniform boundness of the solutions, which is central to the existence and regularity results. First, from the perspective of the value function in the stochastic optimal control problems, we prove the Lipschitz continuity and the semiconcavity for the solutions of the Hamilton-Jacobi equations (HJE). Then the existence of the weak solutions for the degenerate systems is obtained via a vanishing viscosity method. Furthermore, by constructing an auxiliary function, we conclude the regularity of the viscosity solution for the HJE in the almost everywhere sense.