Heat Kernel Estimates and Homogenization for Asymptotically Lower Dimensional Processes on Some Nested Fractals

B. M. Hambly*, T. Kumagai

*この研究の対応する著者

研究成果: Article査読

8 被引用数 (Scopus)

抄録

We consider the class of diffusions on fractals first constructed in [12] on the Sierpinski and abc gaskets. We give an alternative construction of the diffusion process using Dirichlet forms and extend the class of fractals considered to some nested fractals. We use the Dirichlet form to deduce Nash inequalities which give upper bounds on the short and long time behaviour of the transition density of the diffusion process. For short times, even though the diffusion lives mainly on a lower dimensional subset of the fractal, the heat flows slowly. For the long time scales the diffusion has a homogenization property in that rescalings converge to the Brownian motion on the fractal.

本文言語English
ページ(範囲)359-397
ページ数39
ジャーナルPotential Analysis
8
4
DOI
出版ステータスPublished - 1998
外部発表はい

ASJC Scopus subject areas

  • 分析

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