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An Extension Problem Related to the Fractional Laplacian
Open accessAbstract
The operator square root of the Laplacian (− ▵)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 article, 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.
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Cited by
What is a fractional derivative?
Ortigueira, M. D., & Tenreiro Machado, J. A. (2015) · Journal of Computational Physics · doi:10.1016/j.jcp.2014.07.019 · Cited by 511
Representations of the fractional d’Alembertian and initial conditions in fractional dynamics
Calcagni, G., & Nardelli, G. (2025) · Chaos, Solitons & Fractals · doi:10.1016/j.chaos.2025.117401 · Cited by 7
Metadata
- Authors
- Caffarelli, L., & Silvestre, L.
- Venue
- Communications in Partial Differential Equations
- Publisher
- Informa UK Limited
- Published
- 2007-08-08
- Volume
- 32
- Issue
- 8
- Pages
- 1245-1260
- ISSN
- 0360-5302 (ISSN-L)
- 1532-4133
- OpenAlex
- W2172034033
- Cited by
- 2,337
- References
- 0
- FWCI
- 18.08
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Caffarelli, L., & Silvestre, L. (2007). An Extension Problem Related to the Fractional Laplacian. Communications in Partial Differential Equations. https://doi.org/10.1080/03605300600987306
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
