Nonlinear commutators for the fractional p-Laplacian and applications

We prove a nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions for the fractional p -Laplacian. This implies that solutions to certain degenerate nonlocal equations are higher differentiable. Also, weakly fractional p -harmonic functions which a priori are less re...

Full description

Saved in:
Bibliographic Details
Published in:Mathematische annalen 2016-10, Vol.366 (1-2), p.695-720
Main Author: Schikorra, Armin
Format: Article
Language:English
Subjects:
Commutators
Harmonic functions
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove a nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions for the fractional p -Laplacian. This implies that solutions to certain degenerate nonlocal equations are higher differentiable. Also, weakly fractional p -harmonic functions which a priori are less regular than variational solutions are in fact classical. As an application we show that sequences of uniformly bounded n s -harmonic maps converge strongly outside at most finitely many points.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-015-1347-0