Scattering of Electromagnetic Waves by Perfectly Conducting Bodies Moving in Vacuum. Part 4. Kinematic Single Layer Potentials

摘要

Kinematic single layer potentials are defined as certain functions generated by the intrinsic objects associated with a smooth motion and a density function defined on the boundary of the space-time track of the motion. These constitute generalization of the classical single layers associated with the Laplace operator. The support, continuity, and differentiability properties of these functions are examined. In particular, it is shown that the partial derivations of kinematic single layer potentials generally exhibit jump discontinuities on the boundary of the space-time track of the generating motion; the interior and exterior limiting values of these partial derivatives at the boundary are derived. (Author)