Local and non-local Dirichlet forms on the Sierpiński carpet-Reference-Cited by-同舟云学术

Local and non-local Dirichlet forms on the Sierpiński carpet

Published:2019-05-09 Issue:6 Volume:372 Page:3985-4030
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Grigor’yan Alexander,Yang Meng

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.

Funder

Deutsche Forschungsgemeinschaft

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/tran/2019-372-06/S0002-9947-2019-07753-X/tran7753_AM.pdf

Reference40 articles.

1. Energy inequalities for cutoff functions and some applications;Andres, Sebastian;J. Reine Angew. Math.,2015

2. Diffusions on fractals;Barlow, Martin T.,1998

3. Analysis on the Sierpinski carpet;Barlow, M. T.,2013

4. The construction of Brownian motion on the Sierpiński carpet;Barlow, Martin T.;Ann. Inst. H. Poincar\'{e} Probab. Statist.,1989

5. On the resistance of the Sierpiński carpet;Barlow, M. T.;Proc. Roy. Soc. London Ser. A,1990

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