R. Shimizu

most citedConstruction of

p

-energy and associated energy measures on Sierpiński carpets

12 citations · 13 across the 2 of their papers we have counts for

collaborators

2 papers

math.MG2023★ 1 cited

First-order Sobolev spaces, self-similar energies and energy measures on the Sierpiński carpet

Mathav Murugan, Ryosuke Shimizu

We construct and investigate $(1, p)$ -Sobolev space, $p$ -energy, and the corresponding $p$ -energy measures on the planar Sierpiński carpet for all $p \in (1, \infty)$ . Our method i…

math.MG2021★ 12 cited

Construction of $p$ -energy and associated energy measures on Sierpiński carpets

Ryosuke Shimizu

We establish the existence of a scaling limit $E_{p}$ of discrete $p$ -energies on the graphs approximating generalized Sierpiński carpets for $p > \dim_{\text{ARC}}(\textsf…

First-order Sobolev spaces, self-similar energies and energy measures on the Sierpiński carpet

Construction of p-energy and associated energy measures on Sierpiński carpets

Construction of $p$ -energy and associated energy measures on Sierpiński carpets