Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 248, pp. 119.
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 subdomains, 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,
socalled BeppoLevi 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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