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    On idealized electromagnetic singularities in arbitrary nonrelativistic motion
    (Maltepe Üniversitesi, 2009) Polat, Burak
    In this talk we present the distributional derivatives in space (gradient, divergence, curl and Laplacian) and in time of generalized functions whose singular parts are concentrated on an arbitrary surface, an arbitrary space curve or a point in arbitrary nonrelativistic motion. Such generalized functions are described in a Schwartz-Sobolev space setting and represent arbitrary sources or field quantities in the equations of mathematical physics. Their regular components are locally integrable functions in the Lebesgue sense and their singular components are assumed to be constructed via the temporal and spatial derivatives of the Dirac-delta distribution of every order. We illustrate the applications of these mathematical tools to the field equations of classical electrodynamics under the postulation that they apply in the sense of distributions. The results cover initial, boundary/continuity, edge and tip conditions for concentrated sources in arbitrary nonrelativistic motion.