Construction of Local Regular Dirichlet Form on the Sierpiński Gasket using $\Gamma$-Convergence

Abstract

We construct a self-similar local regular Dirichlet form on the Sierpiński 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 Sierpiński gasket and the Sierpiński carpet.

16 pages