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First-Order Mean Field Games with Time-Measurable and $C ^{1,1}$ Hamiltonians: Analysis and Approximation

Elisabetta Carlini, Valentina Coscetti, Francisco J. Silva · 2026 · arXiv

DOI: 10.48550/arXiv.2610.28335 · open-access PDF

Korean

우리는 낮은 정규성의 두 출처를 가진 첫 번째 계층, 비 로컬 중간 필드 게임 (MFG) 시스템의 클래스에 대한 수적 프레임 워크를 소개하고 분석합니다 : 시간에 의존하는 데이터는 단순히 측정할 수 있으며, Hamiltonian은 단지 클래스 $C^{1,1}$에 대한 동기 변수입니다. 제안 된 방법은 Hamilton--Jacobi--Bellman 균형의 반 Lagrangian 접근과 연속성 균형의 Lagrange--Galerkin 판단을 결합합니다.

Machine translation (Meta M2M100); the English original follows.

Abstract

We introduce and analyze a numerical framework for a class of first-order, non-local Mean Field Game (MFG) systems with two sources of low regularity: the time-dependent data are merely measurable, and the Hamiltonian is only of class $C^{1,1}$ with respect to the momentum variable. The proposed method combines a semi-Lagrangian approximation of the Hamilton--Jacobi--Bellman equation with a Lagrange--Galerkin discretization of the continuity equation. Temporal measurability is handled by averaging the data over the time-grid intervals and using the stability theory of $L^1$-viscosity solutions

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