Existence of a unique solution to an elliptic partial differential equation
| dc.contributor.author | Denny, Diane | |
| dc.date.accessioned | 2021-12-03T19:57:23Z | |
| dc.date.available | 2021-12-03T19:57:23Z | |
| dc.date.issued | 2019-09-26 | |
| dc.description.abstract | The purpose of this article is to prove the existence of a unique classical solution to the quasilinear elliptic equation -∇ ∙ (α(u)∇u) = ƒ for x ∈ Ω, which satisfies the condition that u(x0) = u0 at a given point x0 ∈ Ω, under the boundary condition n(x) ∙ ∇u(x) = 0 for x ∈ ∂Ω where n(x) is the outward unit normal vector and where 1 / |Ω| ∫Ω ƒ dx = 0. The domain Ω ⊂ ℝN is a bounded, connected, open set with a smooth boundary, and N = 2 or N = 3. The key to the proof lies in obtaining a priori estimates for the solution. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 13 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Denny, D. L. (2019). Existence of a unique solution to an elliptic partial differential equation. <i>Electronic Journal of Differential Equations, 2019</i>(110), pp. 1-13. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15004 | |
| 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, 2019, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Existence | |
| dc.subject | Uniqueness | |
| dc.subject | Quasilinear | |
| dc.subject | Elliptic | |
| dc.title | Existence of a unique solution to an elliptic partial differential equation | |
| dc.type | Article |