Equivalent Semi-Norms of Non-Local Dirichlet Forms on the Sierpiński Gasket and Applications

Abstract

We construct equivalent semi-norms of non-local Dirichlet forms on the Sierpiński gasket and apply these semi-norms to a convergence problem and a trace problem. We also construct explicitly a sequence of non-local Dirichlet forms with jumping kernels equivalent to $|x-y{|}^{-\alpha -\beta }$ that converges exactly to local Dirichlet form.

18 pages

References in corpus (2)

• Random walks and induced Dirichlet forms on self-similar sets
• Determination of the Walk Dimension of the Sierpiński Gasket Without Using Diffusion

Cited by in corpus (1)

• Heat kernel-based p-energy norms on metric measure spaces