Zobrazeno 1 - 10
of 54
pro vyhledávání: '"primary: 31e05"'
We prove a generalized version of the $3G$ Principle for Green's functions on bounded inner uniform domains in a wide class of Dirichlet spaces. In particular, our results apply to higher-dimensional fractals such as Sierpinski carpets in $\mathbf{R}
Externí odkaz:
http://arxiv.org/abs/2412.18671
Autor:
Shimizu, Ryosuke
In the spirit of the ground-breaking result of Bourgain--Brezis--Mironescu, we establish some characterizations of Sobolev functions in metric measure spaces including fractals like the Vicsek set, the Sierpi\'{n}ski gasket and the Sierpi\'{n}ski car
Externí odkaz:
http://arxiv.org/abs/2410.15317
Autor:
Cho, Soobin
We study weak Harnack inequality and a priori H\"older regularity of harmonic functions for symmetric nonlocal Dirichlet forms on metric measure spaces with volume doubling condition. Our analysis relies on three main assumptions: the existence of a
Externí odkaz:
http://arxiv.org/abs/2403.16853
In this note, we construct a Dirichlet-to-Neumann map, from a Besov space of functions, to the dual of this class. The Besov spaces are of functions on the boundary of a bounded, locally compact uniform domain equipped with a doubling measure support
Externí odkaz:
http://arxiv.org/abs/2403.06042
Autor:
Hino, Masanori
Publikováno v:
From Classical Analysis to Analysis on Fractals: A Tribute to Robert Strichartz, Volume 1, pp. 251-263, Appl. Numer. Harmon. Anal., Birkh\"auser, Cham, 2023
We discuss quantitative estimates of the local spectral dimension of the two-dimensional Sierpinski gasket. The present arguments were inspired by a previous study of the distribution of the Kusuoka measure by R. Bell, C.-W. Ho, and R. S. Strichartz
Externí odkaz:
http://arxiv.org/abs/2211.02827
Given a bounded finely open set $V$ and a function $f$ on the fine boundary of $V$, we introduce four types of upper Perron solutions to the nonlinear Dirichlet problem for $p$-energy minimizers, $1
Externí odkaz:
http://arxiv.org/abs/2209.01150
Publikováno v:
J. Differential Equations 365 (2023), 812-831
In this paper, several convergence results for fine $p$-(super)minimizers on quasiopen sets in metric spaces are obtained. For this purpose, we deduce a Caccioppoli-type inequality and local-to-global principles for fine $p$-(super)minimizers on quas
Externí odkaz:
http://arxiv.org/abs/2206.02697
Autor:
Forrest, Zachary, Freeman, Robert D.
We present a new proof for the equivalence of potential theoretic weak solutions and viscosity solutions to the $\texttt{p}(\cdot)$-Laplace equation in $\mathbb{R}^n$. The proof of the equivalence in the variable exponent case in Euclidean space was
Externí odkaz:
http://arxiv.org/abs/2205.08612
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:
Potential Anal. 59 (2023), 1117-1140 (Open choice)
We initiate the study of fine $p$-(super)minimizers, associated with $p$-harmonic functions, on finely open sets in metric spaces, where $1 < p < \infty$. After having developed their basic theory, we obtain the $p$-fine continuity of the solution of
Externí odkaz:
http://arxiv.org/abs/2106.13738