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Applied Analysis
Seminar information archive ～07/02｜Next seminar｜Future seminars 07/03～
| Date, time & place | Thursday 16:00 - 17:30 002Room #002 (Graduate School of Math. Sci. Bldg.) |
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2024/07/18
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Ryosuke SHIMIZU (Waseda University)
Construction of a p-energy form and p-energy measures on the Sierpiński carpet (Japanese)
Ryosuke SHIMIZU (Waseda University)
Construction of a p-energy form and p-energy measures on the Sierpiński carpet (Japanese)
[ Abstract ]
In this talk, I will propose a new way of constructing the (1,p)-Sobolev space, p-energy functional and p-energy measures on the Sierpinski carpet for all p∈(1,∞). Our approach is mainly based on an idea in the work by Kusuoka--Zhou (1992), where the canonical regular Dirichlet forms (Brownian motions) on some self-similar sets are constructed as scaling limits of discrete 2-energy forms. I will also explain some results related to the Ahlfors regular conformal dimension, which coincides with the critical value p whether our (1,p)-Sobolev space is embedded in the set of continuous functions. This is based on joint work with Mathav Murugan (The University of British Columbia).
In this talk, I will propose a new way of constructing the (1,p)-Sobolev space, p-energy functional and p-energy measures on the Sierpinski carpet for all p∈(1,∞). Our approach is mainly based on an idea in the work by Kusuoka--Zhou (1992), where the canonical regular Dirichlet forms (Brownian motions) on some self-similar sets are constructed as scaling limits of discrete 2-energy forms. I will also explain some results related to the Ahlfors regular conformal dimension, which coincides with the critical value p whether our (1,p)-Sobolev space is embedded in the set of continuous functions. This is based on joint work with Mathav Murugan (The University of British Columbia).
