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

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.