Zobrazeno 1 - 10
of 74
pro vyhledávání: '"Bjoern Anders"'
For nonlinear operators of fractional $p$-Laplace type, we consider two types of solutions to the nonlocal Dirichlet problem: Sobolev solutions based on fractional Sobolev spaces and Perron solutions based on superharmonic functions. These solutions
Externí odkaz:
http://arxiv.org/abs/2406.05994
Autor:
Björn, Anders, Björn, Jana
We study the condenser capacity $\mathrm{cap}_p(E,\Omega)$ on \emph{unbounded} open sets $\Omega$ in a proper connected metric space $X$ equipped with a locally doubling measure supporting a local $p$-Poincar\'e inequality, where $1
Externí odkaz:
http://arxiv.org/abs/2310.05702
Autor:
Björn, Anders, Björn, Jana
Publikováno v:
Math. Z. 305 (2023), Paper No. 41, 26 pp. (Open choice)
We obtain precise estimates, in terms of the measure of balls, for the Besov capacity of annuli and singletons in complete metric spaces. The spaces are only assumed to be uniformly perfect with respect to the centre of the annuli and equipped with a
Externí odkaz:
http://arxiv.org/abs/2304.01803
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
Publikováno v:
J. Math. Anal. Appl. 539 (2024), Paper No. 128483, 28 pp. (Open choice)
A metric space $X$ is called a \emph{bow-tie} if it can be written as $X=X_{+} \cup X_{-}$, where $X_{+} \cap X_{-}=\{x_0\}$ and $X_{\pm} \ne \{x_0\}$ are closed subsets of $X$. We show that a doubling measure $\mu$ on $X$ supports a $(q,p)$--Poincar
Externí odkaz:
http://arxiv.org/abs/2202.07491
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 November 2024 539(1) Part 2
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
Publikováno v:
Rev. Mat. Iberoam. 39 (2023), 1143--1180 (open access)
We study removable sets for Newtonian Sobolev functions in metric measure spaces satisfying the usual (local) assumptions of a doubling measure and a Poincar\'e inequality. In particular, when restricted to Euclidean spaces, a closed set $E\subset \m
Externí odkaz:
http://arxiv.org/abs/2105.09012
Autor:
Björn, Anders
Publikováno v:
Nonlinear Anal. 222 (2022), Paper No. 112906, 16 pp. (Open choice)
It is well known that sets of $p$-capacity zero are removable for bounded $p$-harmonic functions, but on metric spaces there are examples of removable sets of positive capacity. In this paper, we show that this can happen even on unweighted $\mathbf{
Externí odkaz:
http://arxiv.org/abs/2102.08681