Variational formulations for transmission problems of the electromagnetic field

Abstract

The subject of this article is a review of all possible transmission problems for electromagnetic phenomena. In particular, we study the case of a perfect dielectric and a perfect conductor via a (formal) limit with conductivity approaching zero or infinity and discuss the expected regularity of the involved unknowns. Finally, we formulate equivalent variational formulations for each considered problem.

Keywords:

• Maxwell equations
• variational formulation
• transmission condition

AMS Subject Classifications:

• 78A25
• 35Q61