Jana Björn

activity

20122026

most citedPrime ends for domains in metric spaces

43 citations · 328 across the 35 of their papers we have counts for

collaborators

35 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★ 1 cited

Behaviour at infinity for solutions of a mixed boundary value problem via inversion

Jana Björn, Abubakar Mwasa

We study a mixed boundary value problem for the quasilinear elliptic equation $div A (x, \nabla u (x)) = 0$ in an open infinite circular half-cylinder with prescri…

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.AP2020★ 2 cited

Mixed boundary value problem for $p$ -harmonic functions in an infinite cylinder

Jana Björn, Abubakar Mwasa

We study a mixed boundary value problem for the $p$ -Laplace equation $Δ_{p} u = 0$ in an open infinite circular half-cylinder with prescribed Dirichlet boundary data on a part of the b…

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★ 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.AP2016★ 2 cited

Dichotomy of global capacity density in metric measure spaces

Hiroaki Aikawa, Anders Björn, Jana Björn +1

The variational capacity cap_p in Euclidean spaces is known to enjoy the density dichotomy at large scales, namely that for every subset E of R^n, inf_{x in R^n} (cap_p(E \cap B(x,…

math.AP2016★ 7 cited

The Dirichlet problem for p-harmonic functions with respect to arbitrary compactifications

Anders Björn, Jana Björn, Tomas Sjödin

We study the Dirichlet problem for p-harmonic functions on metric spaces with respect to arbitrary compactifications. A particular focus is on the Perron method, and as a new appro…

math.FA2015★ 14 cited

Quasiopen and p-path open sets, and characterizations of quasicontinuity

Anders Björn, Jana Björn, Jan Malý

In this paper we give various characterizations of quasiopen sets and quasicontinuous functions on metric spaces. For complete metric spaces equipped with a doubling measure suppor…

math.AP2015★ 6 cited

The Petrovski\uı criterion and barriers for degenerate and singular p-parabolic equations

Anders Björn, Jana Björn, Ugo Gianazza

In this paper we obtain sharp Petrovskii criteria for the p-parabolic equation, both in the degenerate case p>2 and the singular case 1<p<2. We also give an example of an irregular…

math.AP2015★ 4 cited

Minima of quasisuperminimizers

Anders Björn, Jana Björn, Riikka Korte

Let u_i be a Q_i-quasisuperminimizer, i=1,2, and u=min{u_1,u_2}, where 1 <= Q_1 <= Q_2. Then u is a quasisuperminimizer, and we improve upon the known upper bound (due to Kinnunen…

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

Behaviour at infinity for solutions of a mixed boundary value problem via inversion

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

Mixed boundary value problem for p-harmonic functions in an infinite cylinder

Bounded geometry and p-harmonic functions under uniformization and hyperbolization

Boundary regularity for the porous medium equation

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

Dichotomy of global capacity density in metric measure spaces

The Dirichlet problem for p-harmonic functions with respect to arbitrary compactifications

Quasiopen and p-path open sets, and characterizations of quasicontinuity

The Petrovski\uı criterion and barriers for degenerate and singular p-parabolic equations

Minima of quasisuperminimizers

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

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

Mixed boundary value problem for $p$ -harmonic functions in an infinite cylinder

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