On The Mean Field Games System With the Lateral Cauchy Data via Carleman Estimates

2023/03/14 by Klibanov, Michael V., Li, Jingzhi, Liu, Hongyu · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.07556

Abstract

The second order Mean Field Games system (MFGS) in a bounded domain with the lateral Cauchy data is considered. This means that both Dirichlet and Neumann boundary data for the solution the MFGS are given. Two Hölder stability estimates for two slightly diffeent cases are derived. These estimates indicate how stable the solution of the MFGS is with respect to the possible noise in the lateral Cauchy data. Our stability estimates imply uniqueness. The key mathematical apparatus is the apparatus of two new Carleman estimates.

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