Convergence and local-to-global results for p-superminimizers on quasiopen sets

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 and local-to-global principles for fine p-(super)minimizers on quasiopen sets. A substantial part of these considerations...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Journal of Differential Equations 2023-08, Vol.365, p.812-831
Hauptverfasser:	Björn, Anders, Björn, Jana, Latvala, Visa
Format:	Artikel
Sprache:	eng
Schlagworte:	Caccioppoli inequality Convergence of fine p-superminimizers Fine supersolution Finely open set Nonlinear fine potential theory Quasiopen set
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	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 and local-to-global principles for fine p-(super)minimizers on quasiopen sets. A substantial part of these considerations is to show that the functions belong to a suitable local fine Sobolev space. We prove our results for a complete metric space equipped with a doubling measure supporting a p-Poincaré inequality with 1
ISSN:	0022-0396 1090-2732 1090-2732
DOI:	10.1016/j.jde.2023.05.009