Optimal convergence rates in periodic homogenization of nonconvex Hamilton--Jacobi equations

Abstract

We study the convergence rates in periodic homogenization of general nonconvex, coercive Hamilton--Jacobi equations. We show that the optimal convergence rate is $O({\epsilon }^{1/2})$ in one dimension, $O({\epsilon }^{1/3})$ in two dimensions (up to a logarithmic factor), and $O({\epsilon }^{1/3})$ in dimension three or higher.

During an early exploratory stage, we used OpenAI's GPT-5.6 Sol, through a series of chats, to suggest possible choices of Hamiltonians. These exchanges provided some preliminary directions, but none of the first AI-generated constructions or arguments was used in the final manuscript