Global Lipschitz stability for an inverse coefficient problem for a mean field game system

TL;DR

This paper establishes the global Lipschitz stability for an inverse problem in mean field game systems, using Carleman estimates to determine a spatially varying coefficient from partial data.

Contribution

It introduces a novel stability result for inverse coefficient problems in mean field games using Carleman estimates with different norms.

Findings

Proves global Lipschitz stability for the inverse problem.

Uses Carleman estimates to handle partial data.

Applicable to arbitrary subdomains over time.

Abstract

For an inverse coefficient problem of determining a state-varying factor in the corresponding Hamiltonian for a mean field game system, we prove the global Lipschitz stability by spatial data of one component and interior data in an arbitrarily chosen subdomain over a time interval. The proof is based on Carleman estimates with different norms.