  We study minimal energy problems for strongly singular Riesz kernels on a
manifold. Based on the spatial energy of harmonic double layer potentials, we
are motivated to formulate the natural regularization of such problems by
switching to Hadamard's partie finie integral operator which defines a strongly
elliptic pseudodifferential operator on the manifold. The measures with finite
energy are shown to be elements from the corresponding Sobolev space, and the
associated minimal energy problem admits a unique solution. We relate our
continuous approach also to the discrete one, which has been worked out earlier
by D.P. Hardin and E.B. Saff.
