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arXiv · 1506.02380

Nonlinear commutators for the fractional p-Laplacian and applications

Armin Schikorra
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Abstract

We prove a nonlocal, nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions. For the fractional $p$-Laplace operator it implies that solutions to certain degenerate nonlocal equations are higher differentiable. Also, weak 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.

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Armin Schikorra. 2015-06-08. Nonlinear commutators for the fractional p-Laplacian and applications. https://doi.org/10.1007/s00208-015-1347-0

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