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math.OC2025
A semi-Lagrangian method for solving state constraint Mean Field Games in Macroeconomics
Fabio Camilli, Qing Tang, Yong-shen Zhou
We study continuous-time heterogeneous agent models cast as Mean Field Games, in the Aiyagari-Bewley-Huggett framework. The model couples a Hamilton-Jacobi-Bellman equation for ind…
math.AP2025
Li-Yau inequality and related properties on metric star graphs
Fabio Camilli
We prove a Li-Yau gradient estimate for positive solutions to the heat equation defined on a metric star graph $\mG$ given by the heat kernel formula. As consequence, we derive a H…