6 papers
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 -fractional -Laplacian type in open subsets of . We investigate how the boundary regularity of solutions…
Preserving Besov (fractional Sobolev) energies under sphericalization and flattening
Anders Björn, Jana Björn, Riikka Korte +2
We introduce a new sphericalization mapping for metric spaces that is applicable in very general situations, including totally disconnected fractal type sets. For an unbounded comp…
Doubling measures and Poincaré inequalities for sphericalizations of metric spaces, with applications to -harmonic functions in unbounded domains
Anders Björn, Anders Björn, Jana Björn +2
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…
Uniqueness and nonuniqueness of -harmonic Green functions on weighted and metric spaces
Anders Björn, Jana Björn, Sylvester Eriksson-Bique +1
We study uniqueness of -harmonic Green functions in domains in a complete metric space equipped with a doubling measure supporting a -Poincaré inequality, with $1<p<\in…
Non-quasicontinuous Newtonian functions and outer capacities based on Banach function spaces
Anders Björn, Jana Björn, Lukáš Malý
We construct various examples of Sobolev-type functions, defined via upper gradients in metric spaces, that fail to be quasicontinuous or weakly quasicontinuous. This is done with…
Condenser capacities and capacitary potentials for unbounded sets, and global -harmonic Green functions on metric spaces
Anders Björn, Jana Björn
We study the condenser capacity on \emph{unbounded} open sets in a proper connected metric space equipped with a locally doubling measure supporting…