Constrained Gauss variational problem for condensers with touching plates
arXiv:1505.02596
Abstract
We study a constrained minimum energy problem with an external field relative to the Riesz kernel of an arbitrary order for a generalized condenser with touching oppositely-charged plates. Conditions sufficient for the solvability of the problem are obtained. Our arguments are mainly based on the definition of an appropriate metric structure on a set of vector measures associated with a generalized condenser and the establishment of a completeness theorem for the corresponding metric space.
14 pages