Nonlinear commutators for the fractional p-Laplacian and applications

Original · EN

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 n/s-harmonic maps converge strongly outside at most finitely many points.