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| 開催情報 | 木曜日 16:00～17:30 数理科学研究科棟(駒場) 002号室 |
|---|---|
| 担当者 | 石毛 和弘 |
2024年07月18日(木)
16:00-17:30 数理科学研究科棟(駒場) 128号室
清水 良輔 氏 (早稲田大学)
Construction of a p-energy form and p-energy measures on the Sierpiński carpet (Japanese)
清水 良輔 氏 (早稲田大学)
Construction of a p-energy form and p-energy measures on the Sierpiński carpet (Japanese)
[ 講演概要 ]
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).
