Minimal energy problems for strongly singular Riesz kernels
Classical Analysis and ODEs
2016-03-01 v1 Differential Geometry
Abstract
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.
Cite
@article{arxiv.1602.08544,
title = {Minimal energy problems for strongly singular Riesz kernels},
author = {Helmut Harbrecht and Wolfgang L. Wendland and Natalia Zorii},
journal= {arXiv preprint arXiv:1602.08544},
year = {2016}
}
Comments
31 pages, 2 figures