The Poisson equation from non-local to local
| dc.contributor.author | Biccari, Umberto | |
| dc.contributor.author | Hernandez-Santamaria, Victor | |
| dc.date.accessioned | 2022-02-16T20:22:33Z | |
| dc.date.available | 2022-02-16T20:22:33Z | |
| dc.date.issued | 2018-07-17 | |
| dc.description.abstract | We analyze the limiting behavior as s → 1¯ of the solution to the fractional Poisson equation (-∆)s u s = ƒs, x ∈ Ω with homogeneous Dirichlet boundary conditions u s ≡ 0, x ∈ Ωc. We show that lim s→1¯ u s = 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.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 13 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Biccari, U., & Hernández-Santamaría, V. (2018). The Poisson equation from non-local to local. <i>Electronic Journal of Differential Equations, 2018</i>(145), pp. 1-13. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15345 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional Laplacian | |
| dc.subject | Elliptic equations | |
| dc.subject | Weak solutions | |
| dc.title | The Poisson equation from non-local to local | |
| dc.type | Article |