# 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. Electronic Journal of Differential Equations, 2019(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

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