Pseudodifferential operator method in a problem on the diffraction of an electromagnetic wave on a dielectric body
The authors consider the following diffraction problem: a solid body \(\Omega\) with boundary \(\partial\Omega\) of class \(C^\infty\) characterized by a constant permeability \(\mu_0\) and a \(C^\infty\) \(3\times3\) permittivity tensor \(\hat\epsilon\) is placed in free space \({\mathbb R}^3\). One constructs the electromagnetic field \(\mathbf E\), \(\mathbf H\) satisfying the Maxwell equations, the continuity conditions for the tangential field components across the boundary, and the radiation conditions at infinity. The problem of finding this field can be reduced to the solution of a multidimensional singular integral equation. The authors suggest an alternative method based on the theory of pseudodifferential operators (\(\psi\)DO). Such method permits one to obtain a number of results on the solvability of Maxwell equations other than previously known results.
scientific article; zbMATH DE number 6065281