Static Maxwell System in Axially Symmetric Inhomogeneous Media

Abstract

Consider the static Maxwell system

$$ div(\varepsilon E) = 0, rot E = 0 $$

(10.1)

where we suppose that e is a function of the cylindrical radial variable $r = \sqrt {x_1^2 + x_2^2 :} \varepsilon = \varepsilon (r)$ . Two important situations are usually studied: the meridional field and the transverse field.