Anders Björn

activity

20122026

most citedPrime ends for domains in metric spaces

43 citations · 420 across the 43 of their papers we have counts for

collaborators

44 papers

math.AP2026

Liouville theorems and removable sets for bounded $p$ -harmonic and quasiharmonic functions on metric spaces under local assumptions

Anders Björn, Jana Björn

For connected proper metric spaces $X$ , equipped with a locally doubling measure supporting a local $p$ -Poincaré inequality, we completely characterize which compact sets $K$ with…

math.AP2026

Capacities, Wiener criteria and fine continuity for nonlocal nonlinear equations

Anders Björn, Jana Björn, Minhyun Kim

In this paper we study nonlocal nonlinear equations of $s$ -fractional $p$ -Laplacian type in open subsets of $R^{n}$ . We investigate how the boundary regularity of solutions…

math.FA2025

Doubling measures and Poincaré inequalities for sphericalizations of metric spaces, with applications to $p$ -harmonic functions in unbounded domains

Anders Björn, Jana Björn, Xining Li

The identification between the complex plane and the Riemann sphere preserves holomorphic and harmonic functions and is a classical tool. In this paper we consider a similar mappin…

math.AP2023★ 1 cited

Condenser capacities and capacitary potentials for unbounded sets, and global $p$ -harmonic Green functions on metric spaces

Anders Björn, Jana Björn

We study the condenser capacity $cap_{p} (E, Ω)$ on \emph{unbounded} open sets $Ω$ in a proper connected metric space $X$ equipped with a locally doubling measure supporting a…

math.MG2023★ 3 cited

Sharp Besov capacity estimates for annuli in metric spaces with doubling measures

Anders Björn, Jana Björn

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 uniforml…

math.AP2022

The Perron method associated with finely $p$ -harmonic functions on finely open sets

Anders Björn, Jana Björn, Visa Latvala

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 $p$ -ene…

math.AP2022★ 1 cited

Convergence and local-to-global results for $p$ -superminimizers on quasiopen sets

Anders Björn, Jana Björn, Visa Latvala

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…

math.MG2022★ 2 cited

Poincaré inequalities and $A_{p}$ weights on bow-ties

Anders Björn, Jana Björn, Andreas Christensen

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 $X_{\pm} \neq = {x_{0}}$ are closed subsets of $X$ . We…

math.MG2021★ 6 cited

Classification of metric measure spaces and their ends using $p$ -harmonic functions

Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam

By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy $p$ -harmonic and $p$ -quasiharmonic functions, we classify proper metric spaces equipped…

math.AP2021★ 3 cited

The Dirichlet problem for p-minimizers on finely open sets in metric spaces

Anders Björn, Jana Björn, Visa Latvala

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 th…

math.AP2021★ 7 cited

Removable sets for Newtonian Sobolev spaces and a characterization of $p$ -path almost open sets

Anders Björn, Jana Björn, Panu Lahti

We study removable sets for Newtonian Sobolev functions in metric measure spaces satisfying the usual (local) assumptions of a doubling measure and a Poincaré inequality. In partic…

math.AP2021

Removable singularities for bounded $A$ -(super)harmonic and quasi(super)harmonic functions on weighted $R^{n}$

Anders Björn

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…

math.AP2021★ 4 cited

Volume growth, capacity estimates, $p$ -parabolicity and sharp integrability properties of $p$ -harmonic Green functions

Anders Björn, Jana Björn, Juha Lehrbäck

In a complete metric space equipped with a doubling measure supporting a $p$ -Poincaré inequality, we prove sharp growth and integrability results for $p$ -harmonic Green functions a…

math.AP2020★ 4 cited

Resolutivity and invariance for the Perron method for degenerate equations of divergence type

Anders Björn, Jana Björn, Abubakar Mwasa

We consider Perron solutions to the Dirichlet problem for the quasilinear elliptic equation $div A (x, \nabla u) = 0$ in a bounded open set $Ω\subset\mathbf{R}^…

math.MG2020★ 26 cited

Extension and trace results for doubling metric measure spaces and their hyperbolic fillings

Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam

In this paper we study connections between Besov spaces of functions on a compact metric space $Z$ , equipped with a doubling measure, and the Newton--Sobolev space of functions on…

math.AP2019

Semiregular and strongly irregular boundary points for $p$ -harmonic functions on unbounded sets in metric spaces

Anders Björn, Daniel Hansevi

The trichotomy between regular, semiregular, and strongly irregular boundary points for $p$ -harmonic functions is obtained for unbounded open sets in complete metric spaces with a…

math.MG2019★ 6 cited

Bounded geometry and $p$ -harmonic functions under uniformization and hyperbolization

Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam

The uniformization and hyperbolization transformations formulated by Bonk, Heinonen and Koskela in \emph{"Uniformizing Gromov Hyperbolic Spaces"}, Astérisque {\bf 270} (2001), deal…

math.AP2018★ 1 cited

A uniqueness result for functions with zero fine gradient on quasiconnected and finely connected sets

Anders Björn, Jana Björn

We show that every Sobolev function in $W_{loc}^{1, p} (U)$ on a $p$ -quasiopen set $U \subset R^{n}$ with a.e.-vanishing $p$ -fine gradient is a.e.-constant if and only i…

math.AP2018★ 8 cited

Boundary regularity for the porous medium equation

Anders Björn, Jana Björn, Ugo Gianazza +1

We study the boundary regularity of solutions to the porous medium equation $u_{t} = Δ u^{m}$ in the degenerate range $m > 1$ . In particular, we show that in cylinders the Dirichlet probl…

math.AP2017★ 3 cited

The tusk condition and Petrovski criterion for the normalized $p\mspace{1mu}$-parabolic equation

Anders Björn, Jana Björn, Mikko Parviainen

We study boundary regularity for the normalized $p\mspace{1mu}$-parabolic equation in arbitrary bounded domains. Effros and Kazdan (Indiana Univ. Math. J. 20 (1970), 683-693) showe…

math.AP2017★ 5 cited

Tensor products and sums of p-harmonic functions, quasiminimizers and p-admissible weights

Anders Björn, Jana Björn

The tensor product of two p-harmonic functions is in general not p-harmonic, but we show that it is a quasiminimizer. More generally, we show that the tensor product of two quasimi…

math.AP2017

The Kellogg property and boundary regularity for p-harmonic functions with respect to the Mazurkiewicz boundary and other compactifications

Anders Björn

In this paper boundary regularity for p-harmonic functions is studied with respect to the Mazurkiewicz boundary and other compactifications. In particular, the Kellogg property (wh…

math.AP2017★ 14 cited

Poincaré inequalities and Newtonian Sobolev functions on noncomplete metric spaces

Anders Björn, Jana Björn

Let $X$ be a noncomplete metric space satisfying the usual (local) assumptions of a doubling property and a Poincaré inequality. We study extensions of Newtonian Sobolev functions…

math.AP2017★ 18 cited

Local and semilocal Poincaré inequalities on metric spaces

Anders Björn, Jana Björn

We consider several local versions of the doubling condition and Poincaré inequalities on metric spaces. Our first result is that in proper connected spaces, the weakest local assu…

Liouville theorems and removable sets for bounded p-harmonic and quasiharmonic functions on metric spaces under local assumptions

Capacities, Wiener criteria and fine continuity for nonlocal nonlinear equations

Doubling measures and Poincaré inequalities for sphericalizations of metric spaces, with applications to p-harmonic functions in unbounded domains

Condenser capacities and capacitary potentials for unbounded sets, and global p-harmonic Green functions on metric spaces

Sharp Besov capacity estimates for annuli in metric spaces with doubling measures

The Perron method associated with finely p-harmonic functions on finely open sets

Convergence and local-to-global results for p-superminimizers on quasiopen sets

Poincaré inequalities and Ap​ weights on bow-ties

Classification of metric measure spaces and their ends using p-harmonic functions

The Dirichlet problem for p-minimizers on finely open sets in metric spaces

Removable sets for Newtonian Sobolev spaces and a characterization of p-path almost open sets

Removable singularities for bounded A-(super)harmonic and quasi(super)harmonic functions on weighted Rn

Volume growth, capacity estimates, p-parabolicity and sharp integrability properties of p-harmonic Green functions

Resolutivity and invariance for the Perron method for degenerate equations of divergence type

Extension and trace results for doubling metric measure spaces and their hyperbolic fillings

Semiregular and strongly irregular boundary points for p-harmonic functions on unbounded sets in metric spaces

Bounded geometry and p-harmonic functions under uniformization and hyperbolization

A uniqueness result for functions with zero fine gradient on quasiconnected and finely connected sets

Boundary regularity for the porous medium equation

The tusk condition and Petrovski criterion for the normalized $p\mspace{1mu}$-parabolic equation

Tensor products and sums of p-harmonic functions, quasiminimizers and p-admissible weights

The Kellogg property and boundary regularity for p-harmonic functions with respect to the Mazurkiewicz boundary and other compactifications

Poincaré inequalities and Newtonian Sobolev functions on noncomplete metric spaces

Local and semilocal Poincaré inequalities on metric spaces

Liouville theorems and removable sets for bounded $p$ -harmonic and quasiharmonic functions on metric spaces under local assumptions

Doubling measures and Poincaré inequalities for sphericalizations of metric spaces, with applications to $p$ -harmonic functions in unbounded domains

Condenser capacities and capacitary potentials for unbounded sets, and global $p$ -harmonic Green functions on metric spaces

The Perron method associated with finely $p$ -harmonic functions on finely open sets

Convergence and local-to-global results for $p$ -superminimizers on quasiopen sets

Poincaré inequalities and $A_{p}$ weights on bow-ties

Classification of metric measure spaces and their ends using $p$ -harmonic functions

Removable sets for Newtonian Sobolev spaces and a characterization of $p$ -path almost open sets

Removable singularities for bounded $A$ -(super)harmonic and quasi(super)harmonic functions on weighted $R^{n}$

Volume growth, capacity estimates, $p$ -parabolicity and sharp integrability properties of $p$ -harmonic Green functions

Semiregular and strongly irregular boundary points for $p$ -harmonic functions on unbounded sets in metric spaces

Bounded geometry and $p$ -harmonic functions under uniformization and hyperbolization