Minimum Riesz energy problems for a condenser with "touching plates"
Classical Analysis and ODEs
2015-04-16 v1 Complex Variables
Abstract
Minimum Riesz energy problems in the presence of an external field are analyzed for a condenser with touching plates. We obtain sufficient and/or necessary conditions for the solvability of these problems in both the unconstrained and the constrained settings, investigate the properties of minimizers, and prove their uniqueness. Furthermore, characterization theorems in terms of variational inequalities for the weighted potentials are established. The results obtained are illustrated by several examples.
Cite
@article{arxiv.1504.03805,
title = {Minimum Riesz energy problems for a condenser with "touching plates"},
author = {P. D. Dragnev and D. Hardin and E. B. Saff and N. Zorii},
journal= {arXiv preprint arXiv:1504.03805},
year = {2015}
}
Comments
32 pages, 1 figure