Pith. sign in

REVIEW 1 cited by

An extension problem related to the fractional Laplacian

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/0608640 v2 pith:NXMMF2T3 submitted 2006-08-25 math.AP

Luis Caffarelli , Luis Silvestre This is my paper · ORCID
classification math.AP
keywords extensionlaplaciancharacterizationsconditionfractionalintegro-differentialoperatorproblem
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

The operator square root of the Laplacian $(-\lap)^{1/2}$ can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition. In this paper we obtain similar characterizations for general fractional powers of the Laplacian and other integro-differential operators. From those characterizations we derive some properties of these integro-differential equations from purely local arguments in the extension problems.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Lewy-Stampacchia Inequality for the Fractional Laplacian and Its Application to Anomalous Unidirectional Diffusion Equations

    math.AP 2019-09 conditional novelty 6.0 of 10

    For the spectral fractional Laplacian on a bounded domain, obstacle solutions satisfy the Lewy-Stampacchia inequality f ≤ Au ≤ max{f, Aψ}, which yields well-posedness of a fractional unidirectional diffusion equation.

Pith tools