The Limiting Equation for Neumann Laplacians on Shrinking Domains
| dc.contributor.author | Saito, Yoshimi | |
| dc.date.accessioned | 2020-01-07T15:29:08Z | |
| dc.date.available | 2020-01-07T15:29:08Z | |
| dc.date.issued | 2000-04-26 | |
| dc.description.abstract | Let {Ω∊}0<∊ ≤1 be an indexed family of connected open sets in ℝ², that shrinks to a tree Γ as ∊ approaches zero. Let HΩ∊ be the Neumann Laplacian and ƒ∊ be the restriction of an L²(Ω₁) function to Ω∊. For z ∈ ℂ\ [0, ∞), set u∊ = (HΩ∊ - z)-1 ƒ∊. Under the assumption that all the edges of Γ are line segments, and some additional conditions on Ω∊, we show that the limit function u0 = lim∊→0u∊ satisfies a second-order ordinary differential equation on Γ with Kirchhoff boundary conditions on each vertex of Γ. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 25 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Saito, Y. (2000). The limiting equation for Neumann Laplacians on shrinking domains. <i>Electronic Journal of Differential Equations, 2000</i>(31), pp. 1-25. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/9138 | |
| dc.language.iso | en | |
| dc.publisher | Southwest 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, 2000, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Neumann Laplacian | |
| dc.subject | Tree | |
| dc.subject | Shrinking domains | |
| dc.title | The Limiting Equation for Neumann Laplacians on Shrinking Domains | |
| dc.type | Article |