A trace theorem for Dirichlet forms on fractals

Masanori Hino, Takashi Kumagai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)578-611
Number of pages34
JournalJournal of Functional Analysis
Issue number2
Publication statusPublished - 2006 Sept 15
Externally publishedYes


  • Besov spaces
  • Diffusions on fractals
  • Dirichlet forms
  • Lipschitz spaces
  • Self-similar sets
  • Sierpinski carpets
  • Trace theorem

ASJC Scopus subject areas

  • Analysis


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