Open this publication in new window or tab >>2023 (English)In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 59, p. 1117-1140Article in journal (Refereed) Published
Abstract [en]
We initiate the study of fine p-(super)minimizers, associated with p-harmonic functions, on finely open sets in metric spaces, where
infinity. After having developed their basic theory, we obtain the p-fine continuity of the solution of the Dirichlet problem on a finely open set with continuous Sobolev boundary values, as a by-product of similar pointwise results. These results are new also on unweighted
. We build this theory in a complete metric space equipped with a doubling measure supporting a p-Poincaré inequality.
Place, publisher, year, edition, pages
Springer, 2023
Keywords
Dirichlet problem; Doubling measure; Fine continuity; Fine p-minimizer; Fine p-superminimizer; Fine supersolution; Finely open set; Metric space; Nonlinear fine potential theory; Poincare inequality; Quasiopen set
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-185264 (URN)10.1007/s11118-022-09996-7 (DOI)000792530600001 ()
Note
Funding Agencies|Linkoping University; Swedish Research Council [2016-03424, 2020-04011, 621-2014-3974, 2018-04106]
2022-05-242022-05-242023-11-02Bibliographically approved