18 citations · 96 across the 15 of their papers we have counts for
15 papers
Quasicontinuity of functions and the Vitali-Carathéodory property on general metric spaces
Anders Björn, Jana Björn
This note is a follow up on our recent paper with L. Malý (to appear in Rev. Mat. Complut.). We provide a simple example of a compact metric space for which $L^\infty…
Barriers, Barenblatt solutions and regularity of soda can domains for the heat equation and nonlinear -parabolic equations
Anders Björn, Jana Björn
In this paper we study when the origin is a regular (or irregular) boundary point for the so-called soda can domains of the type \[ Θ_{l,θ}:= \{(x,t) \in \mathbf{R}^{n+1}:…
Boundary regularity and Wiener-type criteria at infinity for nonlinear elliptic equations of -Laplace type
Anders Björn, Jana Björn, David Manolis
We study boundary regularity at the infinity point for nonlinear elliptic equations of -Laplace type in unbounded open sets . We con…
Semiregular and strongly irregular boundary points for nonlocal Dirichlet problems
Anders Björn, Jana Björn, Minhyun Kim
In this paper we study nonlocal nonlinear equations of fractional -Laplacian type on . We show that the irregular boundary points for the Dirichlet problem can…
Perron solutions and boundary regularity for nonlocal nonlinear Dirichlet problems
Anders Björn, Jana Björn, Minhyun Kim
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 an…
Boundary estimates and a Wiener criterion for the fractional Laplacian
Jana Björn
Using the Caffarelli--Silvestre extension, we show for a general open set $\Om\subset\R^n$ that a boundary point is regular for the fractional Laplace equation , $…
The quasisuperminimizing constant for the minimum of two quasisuperminimizers in R^n
Anders Björn, Jana Björn, Ismail Mirumbe
It was shown in Björn--Björn--Korte ("Minima of quasisuperminimizers", Nonlinear Anal. 155 (2017), 264-284) that is a -quasisuperminimizer if $u_…
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 on a -quasiopen set with a.e.-vanishing -fine gradient is a.e.-constant if and only i…
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…
Poincaré inequalities and Newtonian Sobolev functions on noncomplete metric spaces
Anders Björn, Jana Björn
Let 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…
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…
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 and in metric spaces, primarily under the assumptions of an annula…
Sharp exponents and a Wiener type condition for boundary regularity of quasiminimizers
Jana Björn
We obtain a sufficient condition for boundary regularity of quasiminimizers of the p-energy integral in terms of a Wiener type sum of power type. The exponent in the sum is indepen…
Sharp capacity estimates for annuli in weighted R^n and in metric spaces
Anders Björn, Jana Björn, Juha Lehrbäck
We obtain estimates for the nonlinear variational capacity of annuli in weighted R^n and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all…
The variational capacity with respect to nonopen sets in metric spaces
Anders Björn, Jana Björn
We pursue a systematic treatment of the variational capacity on metric spaces and give full proofs of its basic properties. A novelty is that we study it with respect to nonopen se…