Applied Analysis

Seminar information archive ~07/20Next seminarFuture seminars 07/21~

Date, time & place Thursday 16:00 - 17:30 002Room #002 (Graduate School of Math. Sci. Bldg.)

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)
[ 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 $p \in (1,\infty)$. 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).