A trace theorem for Dirichlet forms on fractals
A trace theorem for Dirichlet forms on fractals
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DOI：
10.1016/j.jfa.2006.05.012
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发表时间：
2005-10
影响因子：
1.7
通讯作者：
M. Hino;T. Kumagai
中科院分区：
文献类型：
--
作者：
M. Hino;T. Kumagai
考虑了自相似集上的自相似Dirichlet型到自相似子集的迹定理。特别是，我们的特征域的Dirichlet形式Sierpinski垫片和Sierpinski地毯的边界，其中的边界表示的三角形和正方形，限制垫片和地毯的痕迹。作为一个应用，我们构造扩散过程的分形集合称为分形场。这些过程表现为场的每个分形分量内的适当的分形扩散。
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.