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Minimal energy problems for strongly singular Riesz kernels

Harbrecht, Helmut and Wendland, Wolfgang L. and Zorii, Natalia. (2018) Minimal energy problems for strongly singular Riesz kernels. Mathematical News / Mathematische Nachrichten, 291 (1). pp. 55-85.

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Official URL: http://edoc.unibas.ch/58934/

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Abstract

We study minimal energy problems for strongly singular Riesz kernels math formula, where math formula and math formula, considered for compact math formula-dimensional math formula-manifolds Γ immersed into math formula. Based on the spatial energy of harmonic double layer potentials, we are motivated to formulate the natural regularization of such minimization problems by switching to Hadamard's partie finie integral operator which defines a strongly elliptic pseudodifferential operator of order math formula on Γ. The measures with finite energy are shown to be elements from the Sobolev space math formula, math formula, and the corresponding 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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Wiley
ISSN:0025-584X
e-ISSN:1522-2616
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:02 Feb 2018 14:28
Deposited On:02 Feb 2018 14:28

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