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dc.contributor.authorBiccari, Umberto ( Orcid Icon 0000-0003-0096-5630 )
dc.contributor.authorHernandez-Santamaria, Victor ( )
dc.date.accessioned2022-02-16T20:22:33Z
dc.date.available2022-02-16T20:22:33Z
dc.date.issued2018-07-17
dc.identifier.citationBiccari, U., & Hernández-Santamaría, V. (2018). The Poisson equation from non-local to local. Electronic Journal of Differential Equations, 2018(145), pp. 1-13.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15345
dc.description.abstractWe analyze the limiting behavior as s → 1¯ of the solution to the fractional Poisson equation (-∆)sus = ƒs, x ∈ Ω with homogeneous Dirichlet boundary conditions us ≡ 0, x ∈ Ωc. We show that lims→1¯ us = u, with -∆u = ƒ, x ∈ Ω and u = 0, x ∈ ∂Ω. Our results are complemented by a discussion on the rate of convergence and on extensions to the parabolic setting.
dc.formatText
dc.format.extent13 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectFractional Laplacianen_US
dc.subjectElliptic equationsen_US
dc.subjectWeak solutionsen_US
dc.titleThe Poisson equation from non-local to localen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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