Local and Non-Local Dirichlet Forms on the Sierpi\'nski Carpet
Functional Analysis
2018-11-09 v2
Abstract
We give a purely analytic construction of a self-similar local regular Dirichlet form on the Sierpi\'nski carpet using approximation of stable-like non-local closed forms which gives an answer to an open problem in analysis on fractals.
Cite
@article{arxiv.1706.03318,
title = {Local and Non-Local Dirichlet Forms on the Sierpi\'nski Carpet},
author = {Alexander Grigor'yan and Meng Yang},
journal= {arXiv preprint arXiv:1706.03318},
year = {2018}
}
Comments
36 pages, to appear in Transactions of the American Mathematical Society