Abstract
We continue our investigation of the Gauss variational problem for infinite dimensional vector measures on a locally compact space, associated with a condenser (Ai)i ∈ I. It has been shown by Zorii (Potential Anal 38:397–432, 2013) that, if some of the plates (say Al for l ∈ L) are noncompact then, in general, there exists a vector a = (ai)i ∈ I, prescribing the total charges on Ai, i ∈ I, such that the problem admits no solution. Then, what is a description of the set of all vectors a for which the Gauss variational problem is nevertheless solvable? Such a characterization is obtained for a positive definite kernel satisfying Fuglede’s condition of perfectness; it is given in terms of a solution to an auxiliary extremal problem intimately related to the operator of orthogonal projection onto the convex cone of all nonnegative scalar measures supported by ∪ l ∈ LAl. The results are illustrated by several examples pertaining to the Riesz kernels.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
