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.