Local regularity for nonlocal double phase equations in the Heisenberg group

We prove interior boundedness and Hölder continuity for the weak solutions of nonlocal double phase equations in the Heisenberg group $\mathbb{H}^n$ . This solves a problem raised by Palatucci and Piccinini et al. in 2022 and 2023 for the nonlinear integro-differential problems in Heisenberg setting...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2024-11, p.1-37
Hauptverfasser: Fang, Yuzhou, Zhang, Chao, Zhang, Junli
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We prove interior boundedness and Hölder continuity for the weak solutions of nonlocal double phase equations in the Heisenberg group $\mathbb{H}^n$ . This solves a problem raised by Palatucci and Piccinini et al. in 2022 and 2023 for the nonlinear integro-differential problems in Heisenberg setting. Our proof of the a priori estimates bases on De Giorgi–Nash–Moser theory, where the important ingredients are Caccioppoli-type inequality and Logarithmic estimate. To achieve this goal, we establish a new and crucial Sobolev–Poincaré type inequality in local domain, which may be of independent interest and potential applications.
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2024.89