On The Mean Field Games System With the Lateral Cauchy Data via Carleman Estimates
Analysis of PDEs
2023-11-27 v4
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 H\"older 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.
Keywords
Cite
@article{arxiv.2303.07556,
title = {On The Mean Field Games System With the Lateral Cauchy Data via Carleman Estimates},
author = {Michael V. Klibanov and Jingzhi Li and Hongyu Liu},
journal= {arXiv preprint arXiv:2303.07556},
year = {2023}
}