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dc.contributor.authorDenny, Diane ( )
dc.date.accessioned2021-12-03T19:57:23Z
dc.date.available2021-12-03T19:57:23Z
dc.date.issued2019-09-26
dc.identifier.citationDenny, D. L. (2019). Existence of a unique solution to an elliptic partial differential equation. Electronic Journal of Differential Equations, 2019(110), pp. 1-13.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15004
dc.description.abstractThe 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| ∫ 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.formatText
dc.format.extent13 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectExistenceen_US
dc.subjectUniquenessen_US
dc.subjectQuasilinearen_US
dc.subjectEllipticen_US
dc.titleExistence of a unique solution to an elliptic partial differential equationen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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