High-order convergence rates of periodic homogenization for symmetric L\'evy type operators

Xin Chen; Zhen-Qing Chen; Takashi Kumagai; Jian Wang

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arXiv · 2606.29131

High-order convergence rates of periodic homogenization for symmetric L\'evy type operators

Xin Chen·Zhen-Qing Chen·Takashi Kumagai·Jian Wang

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Abstract

In this paper, we establish higher-order convergence rates of the periodic homogenizatio for symmetric L\'evy-type operators, encompassing the subcritical $\alpha$-stable regime, critical regime, and supercritical diffusive regime. To this end, we develop a systematic framework to decompose the contributions of the underlying jumping kernel across small, intermediate, and large spatial scales -- a strategy tailored to all the aforementioned regimes. To the best of our knowledge, this work represents the first comprehensive study of higher-order convergence rates in the homogenization of non-local operators.

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Xin Chen, Zhen-Qing Chen, Takashi Kumagai, Jian Wang. 2026-06-28. High-order convergence rates of periodic homogenization for symmetric L\'evy type operators. https://arxiv.org/abs/2606.29131

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