Local and non-local Dirichlet forms on the Sierpiński carpet

Grigor’yan, Alexander; Yang, Meng

doi:10.1090/tran/7753

Local and non-local Dirichlet forms on the Sierpiński carpet
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by Alexander Grigor’yan and Meng Yang PDF

Trans. Amer. Math. Soc. 372 (2019), 3985-4030 Request permission

Abstract:

We give a purely analytic construction of a self-similar local regular Dirichlet form on the Sierpiński carpet using approximation of stable-like non-local closed forms which gives an answer to an open problem in analysis on fractals.

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