Denny, Diane2021-12-032021-12-032019-09-26Denny, D. L. (2019). Existence of a unique solution to an elliptic partial differential equation. <i>Electronic Journal of Differential Equations, 2019</i>(110), pp. 1-13.1072-6691https://hdl.handle.net/10877/15004The 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.Text13 pages1 file (.pdf)enAttribution 4.0 InternationalExistenceUniquenessQuasilinearEllipticArticle