Nonlinear commutators for the fractional \(p\)-Laplacian and applications. (English) Zbl 1351.35255
The author proves a nonlinear commutator estimate regarding the transfer of derivatives onto testfunctions for the fractional \(p\)-Laplacian operator. This implies that solutions to certain degenerate nonlocal equations are higher differentiable. Moreover, weakly fractional \(p\)-harmonic functions that are a priori less regular than the variational solutions, are in fact classical. As an application of these results, the author shows that sequences of uniformly bounded \(\frac{n}{s}\)-harmonic maps converge strongly outside at most finitely many points.
Reviewer: Dian K. Palagachev (Bari)
MSC:
| 35R11 | Fractional partial differential equations |
| 35D30 | Weak solutions to PDEs |
| 35B45 | A priori estimates in context of PDEs |
| 35J60 | Nonlinear elliptic equations |
| 47G20 | Integro-differential operators |
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
| 58E20 | Harmonic maps, etc. |
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