An Exterior Neumann Boundary-Value Problem for the Div-Curl System and Applications

Briceyda B. Delgado and Jorge Eduardo Macías-Díaz
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Briceyda B. Delgado: Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20131, Mexico
Jorge Eduardo Macías-Díaz: Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20131, Mexico

Mathematics, 2021, vol. 9, issue 14, 1-25

Abstract: We investigate a generalization of the equation curl w ? = g ? to an arbitrary number n of dimensions, which is based on the well-known Moisil–Teodorescu differential operator. Explicit solutions are derived for a particular problem in bounded domains of R n using classical operators from Clifford analysis. In the physically significant case n = 3 , two explicit solutions to the div-curl system in exterior domains of R 3 are obtained following different constructions of hyper-conjugate harmonic pairs. One of the constructions hinges on the use of a radial integral operator introduced recently in the literature. An exterior Neumann boundary-value problem is considered for the div-curl system. That system is conveniently reduced to a Neumann boundary-value problem for the Laplace equation in exterior domains. Some results on its uniqueness and regularity are derived. Finally, some applications to the construction of solutions of the inhomogeneous Lamé–Navier equation in bounded and unbounded domains are discussed.

Keywords: div-curl system; exterior domains; Neumann boundary-value problem; Lamé–Navier equation; maximum principle; harmonic functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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