Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 248, pp. 1-19.

Title: Electromagnetic transmission problems with a large parameter in
       weighted Sobolev spaces

Author: Jorge Eliecer Ospino (Univ. del Norte, Barranquilla, Colombia)

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.