On the mean field games system with lateral Cauchy data via Carleman estimates
Michael V. Klibanov, Jingzhi Li, Hongyu Liu
Abstract
Abstract The second-order mean field games system (MFGS) in a bounded domain with the lateral Cauchy data are considered. This means that both Dirichlet and Neumann boundary data for the solution of the MFGS are given. Two Hölder stability estimates for two slightly different 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.
Topics & Concepts
Bounded functionCauchy distributionStability (learning theory)MathematicsUniquenessCauchy boundary conditionDomain (mathematical analysis)Mathematical analysisBoundary (topology)Neumann boundary conditionDirichlet distributionApplied mathematicsNoise (video)Field (mathematics)Boundary value problemComputer sciencePure mathematicsArtificial intelligenceImage (mathematics)Machine learningStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringStochastic processes and financial applications