Electromagnetostatic operator, its spectral properties, and application to the problem of distribution of eddy currents (Q1571319)

The author proves a theorem on the general spectral properties of the electromagnetostatic operator and the operators of the Neumann and Maxwell boundary value problems for a bounded simply connected domain \(V\in\mathbb{R}^3\). This theorem appeared when analyzing a pair of harmonic fields in the domaines \(V\) and \(V_1={\mathbb{R}^3}\setminus\overline{V}\) under certain additional conditions imposed on the relation between the normal and tangent components of these fields on the boundary separating \(V\) and \(V_1\). The existence theorem for pairs of such fields is proved. The theorems proved can be applied to the problem of distribution of eddy current.