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

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32 papers · 1 filter

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.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.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.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.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.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…

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.AP2015★ 16 cited

The annular decay property and capacity estimates for thin annuli

Anders Björn, Jana Björn, Juha Lehrbäck

We obtain upper and lower bounds for the nonlinear variational capacity of thin annuli in weighted $R^{n}$ and in metric spaces, primarily under the assumptions of an annula…

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…

math.AP2015★ 13 cited

Sobolev spaces, fine gradients and quasicontinuity on quasiopen sets

Anders Björn, Jana Björn, Visa Latvala

We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space equipped with a doubling measure supporting a p-Poincaré inequality with 1<p<\infty, a…

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

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

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

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

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

Dichotomy of global capacity density in metric measure spaces

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

The annular decay property and capacity estimates for thin annuli

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

Minima of quasisuperminimizers

Sobolev spaces, fine gradients and quasicontinuity on quasiopen sets

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

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

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