A trace theorem for Dirichlet forms on fractals

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• 作者：Masanori Hino and Takashi Kumagai
• 关键词：Trace theorem ; Self-similar sets ; Dirichlet forms ; Diffusions on fractals ; Lipschitz spaces ; Besov spaces ; Sierpinski carpets
• 刊名：Journal of Functional Analysis
• 出版年：2006
• 出版时间：15 September 2006
• 年：2006
• 卷：238
• 期：2
• 页码：578-611
• 全文大小：390 K

文摘

We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on Sierpinski gaskets and Sierpinski carpets to their boundaries, where the boundaries are represented by triangles and squares that confine the gaskets and the carpets. As an application, we construct diffusion processes on a collection of fractals called fractal fields. These processes behave as an appropriate fractal diffusion within each fractal component of the field.