The poisson equation from non-local to local
| dc.contributor.author | Biccari, Umberto | |
| dc.contributor.author | Hernández Santamaría, Víctor | |
| dc.date.accessioned | 2025-01-07T13:24:12Z | |
| dc.date.available | 2025-01-07T13:24:12Z | |
| dc.date.issued | 2018 | |
| dc.date.updated | 2025-01-07T13:24:12Z | |
| dc.description.abstract | We analyze the limiting behavior as s → 1− of the solution to the fractional Poisson equation (−∆)s us = fs, x ∈ Ω with homogeneous Dirichlet boundary conditions us ≡ 0, x ∈ Ωc. We show that lims →1 − us = u, with −∆u = f, 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. | en |
| dc.description.sponsorship | This project received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 694126-DyCon), and from the MTM2017-92996-C2-1-R grant of MINECO (Spain). U. Biccari was partially supported by the Grants MTM2014- 52347 of MINECO (Spain) and FA9550-18-1-0242 of AFOSR (USA) | en |
| dc.identifier.citation | Biccari, U., & Hernández-Santamaría, V. (2018). The poisson equation from non-local to local. Electronic Journal of Differential Equations, 2018(145), 1-13. | |
| dc.identifier.eissn | 1072-6691 | |
| dc.identifier.uri | http://hdl.handle.net/20.500.14454/2193 | |
| dc.language.iso | eng | |
| dc.publisher | Texas State University - San Marcos | |
| dc.rights | © 2018 Texas State University | |
| dc.subject.other | Elliptic equations | |
| dc.subject.other | Fractional laplacian | |
| dc.subject.other | Weak solutions | |
| dc.title | The poisson equation from non-local to local | en |
| dc.type | journal article | |
| dcterms.accessRights | open access | |
| oaire.citation.endPage | 13 | |
| oaire.citation.issue | 145 | |
| oaire.citation.startPage | 1 | |
| oaire.citation.title | Electronic Journal of Differential Equations | |
| oaire.citation.volume | 2018 | |
| oaire.licenseCondition | https://creativecommons.org/licenses/by/4.0/ | |
| oaire.version | VoR |
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