# Local and Non-Local Dirichlet Forms on the Sierpi\'nski Carpet

## TL;DR

This paper constructs a self-similar local Dirichlet form on the Sierpiński carpet through an analytic approach, solving an open problem in fractal analysis by approximating non-local forms.

## Contribution

It introduces a purely analytic method to build a local Dirichlet form on the Sierpiński carpet, addressing an open problem in the analysis of fractals.

## Key findings

- Successfully constructs a local regular Dirichlet form on the Sierpiński carpet.
- Provides an approximation scheme for stable-like non-local forms.
- Answers an open problem in analysis on fractals.

## 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.