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<p>This paper investigates quantitative estimates in elliptic homogenization of non-divergence form with unbounded drifts and an interface, which continues the study of the previous work by Hairer and Manson [Ann. Probab. 39(2011) 648-682], where they investigated the limiting long time/large scale behaviour of such a process under diffusive rescaling. We determine the effective equation and obtain the size estimates of the gradient of Green functions as well as the optimal (in general) convergence rates. The proof relies on transferring the non-divergence form into the divergence-form with the coefficient matrix decaying exponentially to some (different) periodic matrix on the different sides of the interface and investigating this special structure in homogenization of divergence form.</p>

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Quantitative estimates in elliptic homogenization of non-divergence form with unbounded drifts and an interface

  • 期刊论文

  • 发表日期：

    2025年3月24日

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  • Yiping Zhang

摘要

This paper investigates quantitative estimates in elliptic homogenization of non-divergence form with unbounded drifts and an interface, which continues the study of the previous work by Hairer and Manson [Ann. Probab. 39(2011) 648-682], where they investigated the limiting long time/large scale behaviour of such a process under diffusive rescaling. We determine the effective equation and obtain the size estimates of the gradient of Green functions as well as the optimal (in general) convergence rates. The proof relies on transferring the non-divergence form into the divergence-form with the coefficient matrix decaying exponentially to some (different) periodic matrix on the different sides of the interface and investigating this special structure in homogenization of divergence form.