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Mathematische Annalen

, Volume 366, Issue 1–2, pp 695–720 | Cite as

Nonlinear commutators for the fractional p-Laplacian and applications

  • Armin Schikorra
Article

Abstract

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 \(\frac{n}{s}\)-harmonic maps converge strongly outside at most finitely many points.

Mathematics Subject Classification

35D30 35B45 35J60 47G20 35S05 58E20 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Universität BaselBaselSwitzerland

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