Potential Anal https://doi.org/10.1007/s11118-018-9709-3 An Alternative Concept of Riesz Energy of Measures with Application to Generalized Condensers 1 2 Bent Fuglede · Natalia Zorii Received: 29 March 2018 / Accepted: 14 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract In view of a recent example of a positive Radon measure μ on a domain D ⊂ R , n 3, such that μ is of finite energy E (μ) relative to the α-Green kernel g on D, though D α−n the energy of μ − μ relative to the α-Riesz kernel |x − y| ,0 <α 2, is not well D c n defined (here μ is the α-Riesz swept measure of μ onto D = R \ D), we propose a weaker concept of α-Riesz energy for which this defect has been removed. This concept is applied to the study of a minimum weak α-Riesz energy problem over (signed) Radon n c measures on R associated with a (generalized) condenser A = (A ,D ),where A is a 1 1 relatively closed subset of D. A solution to this problem exists if and only if the g-capacity of A is finite, which
Potential Analysis – Springer Journals
Published: May 21, 2018
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