AI 中文总结
该研究针对一般非凸强制型Hamilton--Jacobi方程的周期均匀化问题，推导得出不同维度下的最优收敛速率，完善了非凸情形下的均匀化收敛速率理论。
AI 中文摘要
我们研究一般非凸、强制型Hamilton--Jacobi方程周期均匀化的收敛速率。我们证明最优收敛速率在一维为$O(\varepsilon^{1/2})$，二维为$O(\varepsilon^{1/3})$（至多相差一个对数因子），三维及更高维为$O(\varepsilon^{1/3})$。
英文摘要
We study the convergence rates in periodic homogenization of general nonconvex, coercive Hamilton--Jacobi equations. We show that the optimal convergence rate is $O(\varepsilon^{1/2})$ in one dimension, $O(\varepsilon^{1/3})$ in two dimensions (up to a logarithmic factor), and $O(\varepsilon^{1/3})$ in dimension three or higher.
CommentsDuring 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
