Regularization of the second-order partial derivatives of the Coulomb potential of a point charge

The second-order partial derivatives of the Coulomb potential of a point charge can be regularized using the Coulomb potential of a charge of the oblate spheroidal shape that a moving rest-frame-spherical charge acquires by the Lorentz contraction. This `physical' regularization is shown to be fully equivalent to the standard delta-function identity involving these derivatives.