19 citations · 52 across the 6 of their papers we have counts for
6 papers
The Perron method associated with finely -harmonic functions on finely open sets
Anders Björn, Jana Björn, Visa Latvala
Given a bounded finely open set and a function on the fine boundary of , we introduce four types of upper Perron solutions to the nonlinear Dirichlet problem for -ene…
Convergence and local-to-global results for -superminimizers on quasiopen sets
Anders Björn, Jana Björn, Visa Latvala
In this paper, several convergence results for fine -(super)minimizers on quasiopen sets in metric spaces are obtained. For this purpose, we deduce a Caccioppoli-type inequality…
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 -(super)minimizers, associated with -harmonic functions, on finely open sets in metric spaces, where . After having developed th…
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…
The Cartan, Choquet and Kellogg properties for the fine topology on metric spaces
Anders Björn, Jana Björn, Visa Latvala
We prove the Cartan and Choquet properties for the fine topology on a complete metric space equipped with a doubling measure supporting a -Poincaré inequality, .…
The weak Cartan property for the p-fine topology on metric spaces
Anders Björn, Jana Björn, Visa Latvala
We study the p-fine topology on complete metric spaces equipped with a doubling measure supporting a p-Poincare inequality, 1 < p< oo. We establish a weak Cartan property, which yi…