# Construction of Local Regular Dirichlet Form on the Sierpi\'nski Gasket using $\Gamma$-Convergence

## TL;DR

This paper develops a unified analytic method to construct local regular Dirichlet forms on fractals like the Sierpiński gasket and carpet using $ ext{Gamma}$-convergence, advancing the understanding of analysis on fractals.

## Contribution

It introduces a novel $ ext{Gamma}$-convergence approach to construct local regular Dirichlet forms on fractals, applicable to both the Sierpiński gasket and carpet.

## Key findings

- First unified analytic construction for these fractals
- Uses $ ext{Gamma}$-convergence of stable-like forms
- Applicable to multiple fractal structures

## Abstract

We construct a self-similar local regular Dirichlet form on the Sierpi\'nski gasket using $\Gamma$-convergence of stable-like non-local closed forms. As a continuation of a recent paper by Grigor'yan and the author, we give the first \emph{unified} purely analytic construction of local regular Dirichlet forms that works both on the Sierpi\'nski gasket and the Sierpi\'nski carpet.