English

A trace theorem for Dirichlet forms on fractals

Probability 2007-05-23 v1 Classical Analysis and ODEs

Abstract

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 the Sierpinski gaskets and the Sierpinski carpets to their boundaries, where boundaries mean the triangles and rectangles which confine gaskets and carpets. As an application, we construct diffusion processes on a collection of fractals called fractal fields, which behave as the appropriate fractal diffusion within each fractal component of the field.

Keywords

Cite

@article{arxiv.math/0510553,
  title  = {A trace theorem for Dirichlet forms on fractals},
  author = {Masanori Hino and Takashi Kumagai},
  journal= {arXiv preprint arXiv:math/0510553},
  year   = {2007}
}

Comments

32 pages, 2 figures