Homogenization of anisotropic diffusion on pre-Sierpiński carpets
Shiping Cao, Zhen-Qing Chen, Hua Qiu
Source abstract
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}.
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