Nonlinear commutators for the fractional p-Laplacian and applications

Armin Schikorra

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Nonlinear commutators for the fractional p-Laplacian and applications

Armin Schikorra

Analysis of PDEs · Submitted 8 Jun 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove a nonlocal, nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions.

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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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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We prove a nonlocal, nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions.	contribution 0.57	0.96	0.67	asserted 1.00
s1	For the fractional $p$-Laplace operator it implies that solutions to certain degenerate nonlocal equations are higher differentiable.	interpretation 0.85	0.87	0.30	asserted 0.94
s2	Also, weak fractional $p$-harmonic functions which a priori are less regular than variational solutions are in fact classical.	result 0.94	0.84	0.19	asserted 1.00
s3	As an application we show that sequences of uniformly bounded $\frac{n}{s}$-harmonic maps converge strongly outside at most finitely many points.	result 0.91	0.94	0.11	asserted 1.00

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The paper

Original 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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1 arXiv paper cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites it as background 1 paper

Some results on this subject are contained in the recent papers [ref] and [ref] (see also [ref] ).

Higher Sobolev regularity for the fractional $p-$Laplace equation in the superquadratic case · Aim of the paper · 0.90

What it cites

Cites as background 3 papers

The fractional $p$-Laplacian has recently received quite some interest, for example we refer to [ref] .

Global H\"older regularity for the fractional $p$-Laplacian · Introduction · 0.96
The fractional $p$-Laplacian has recently received quite some interest, for example we refer to [ref] .

The Dirichlet Problem for the fractional p-Laplacian evolution equation · Introduction · 0.96
As a distribution [equation] For an overview on the fractional Laplacian and fractional Sobolev spaces we refer to, e.g., [ref] .

Nonlocal diffusion and applications · Introduction · 1.00

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