Electron. J. Diff. Equ., Vol. 2013 (2013), No. 248, pp. 1-19.

Electromagnetic transmission problems with a large parameter in weighted Sobolev spaces

Jorge Eliecer Ospino

Abstract:
We present an a priori estimate for an electromagnetic transmission problem in unbounded exterior domains in R^3. We consider Maxwell's equations in two sub-domains, the bounded interior representing a conducting material (metal) and the unbounded exterior representing an insulating material (air). The behavior of the solution at infinity is described by means of families of weighted Sobolev spaces, so-called Beppo-Levi spaces [11]. We prove the existence and uniqueness of the solution.

Submitted June 15, 2012. Published November 15, 2013.
Math Subject Classifications: 65N15, 35A35.
Key Words: Electromagnetic transmission problem; weighted Sobolev spaces; a priori estimates.

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Jorge Eliécer Ospino Portillo
Departamento de Matemáticas y Estadística
Fundación Universidad del Norte
Barranquilla, Colombia
email: jospino@uninorte.edu.co

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