发表机构
The Chinese University of Hong Kong; University of Washington; Nanjing University（香港中文大学; 华盛顿大学; 南京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究平面预谢尔宾斯基地毯上各向异性扩散的均匀化问题，证明其弱收敛到谢尔宾斯基地毯上的布朗运动，对相关强均匀化猜想给出肯定回答。
AI 中文摘要
我们研究平面预谢尔宾斯基地毯上各向异性扩散的各向同性恢复问题，该问题此前由Barlow、Hattori、Hattori和Watanabe研究，他们得到了各向异性扩散有效电阻比值的弱均匀化性质。我们证明了这些各向异性扩散弱收敛到谢尔宾斯基地毯上的布朗运动，据此对文献[BHHW]第3页提出的强均匀化猜想给出了肯定回答。
英文摘要
We investigate the restoration of isotropy for anisotropic diffusions on pre-Sierpiński carpets in the plane, a problem previously studied by Barlow, Hattori, Hattori and Watanabe \cite{BHHW} in which they obtained a weak homogenization property for the ratio of effective resistances of the anisotropic diffusions. We establish the weak convergence of these anisotropic diffusions to Brownian motion on the Sierpiński carpet. As a consequence, we give an affirmative answer to the strong homogenization conjecture raised in \cite[p.3]{BHHW}.
