Distributional derivatives on a regular open surface with physical applications

Abstract

The spatial derivatives of Schwartz-Sobolev distributions which display singularities of arbitrary order on an arbitrary regular open surface are investigated. The contributions of the present investigation to literature are i) an approach alternative to the derivation of the distributional derivatives of multilayers by Estrada and Kanwal; ii) an extension of the available results for closed surfaces to open surfaces featuring boundary distributions of arbitrary order. The end results are applied in the distributional investigation of Maxwell equations in presence of single and double layer sources located on a regular open surface.