Brownian Motion Penetrating Fractals: An Application of the Trace Theorem of Besov Spaces

Takashi Kumagai*

*この研究の対応する著者

研究成果: Article査読

34 被引用数 (Scopus)

抄録

For a closed connected set F in Rn, assume that there is a local regular Dirichlet form (a symmetric diffusion process) on F whose domain is included in a Lipschitz space or a Besov space on F. Under some condition for the order of the space and the Newtonian 1-capacity of F, we prove that there exists a symmetric diffusion process on Rn which moves like the process on F and like Brownian motion on Rn outside F. As an application, we will show that when F is a nested fractal or a Sierpinski carpet whose Hausdorff dimension is greater than n-2, we can construct Brownian motion penetrating the fractal. For the proof, we apply the technique developed in the theory of Besov spaces.

本文言語English
ページ(範囲)69-92
ページ数24
ジャーナルJournal of Functional Analysis
170
1
DOI
出版ステータスPublished - 2000 1月 10
外部発表はい

ASJC Scopus subject areas

  • 分析

フィンガープリント

「Brownian Motion Penetrating Fractals: An Application of the Trace Theorem of Besov Spaces」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル