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pro vyhledávání: '"energy measures"'
Autor:
Kajino, Naotaka, Shimizu, Ryosuke
We construct good $p$-energy forms on metric measure spaces as pointwise subsequential limits of Besov-type $p$-energy functionals under certain geometric/analytic conditions. Such forms are often called Korevaar-Schoen $p$-energy forms in the litera
Externí odkaz:
http://arxiv.org/abs/2404.13435
Autor:
Murugan, Mathav, Shimizu, Ryosuke
We construct and investigate $(1, p)$-Sobolev space, $p$-energy, and the corresponding $p$-energy measures on the planar Sierpi\'{n}ski carpet for all $p \in (1, \infty)$. Our method is based on the idea of Kusuoka and Zhou [Probab. Theory Related Fi
Externí odkaz:
http://arxiv.org/abs/2308.06232
Publikováno v:
In Results in Engineering March 2024 21
Autor:
Kajino, Naotaka, Murugan, Mathav
Publikováno v:
The Annals of Probability, 2020 Nov 01. 48(6), 2920-2951.
Externí odkaz:
https://www.jstor.org/stable/26966059
Autor:
Kajino, Naotaka
We present a concrete family of fractals, which we call the (two-dimensional) thin scale irregular Sierpi\'{n}ski gaskets and each of which is equipped with a canonical strongly local regular symmetric Dirichlet form. We prove that any fractal $K$ in
Externí odkaz:
http://arxiv.org/abs/2108.02027
Publikováno v:
In Resources Policy October 2023 86 Part B
Autor:
Hino, Masanori, Yasui, Madoka
We study energy measures of canonical Dirichlet forms on inhomogeneous Sierpinski gaskets. We prove that the energy measures and suitable reference measures are mutually singular under mild assumptions.
Comment: 24 pages, 2 figures, minor revisi
Comment: 24 pages, 2 figures, minor revisi
Externí odkaz:
http://arxiv.org/abs/2106.06705
Autor:
Shimizu, Ryosuke
Publikováno v:
Trans. Amer. Math. Soc. 377 (2024), 951-1032
We establish the existence of a scaling limit $\mathcal{E}_p$ of discrete $p$-energies on the graphs approximating generalized Sierpi\'{n}ski carpets for $p > \dim_{\text{ARC}}(\textsf{SC})$, where $\dim_{\text{ARC}}(\textsf{SC})$ is the Ahlfors regu
Externí odkaz:
http://arxiv.org/abs/2110.13902
Akademický článek
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Publikováno v:
In Soil Dynamics and Earthquake Engineering April 2019 119:454-470