Logarithmic and Riesz Equilibrium for Multiple Sources on the Sphere: The Exceptional Case

DOI10.1007/978-3-319-72456-0_10zbMath1405.31007arXiv1706.09346OpenAlexW2732277901MaRDI QIDQ4611800

Robert S. Womersley, Johann S. Brauchart, Peter D. Dragnev, Edward B. Saff

Publication date: 22 January 2019

Published in: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.09346

zbMATH Keywords

equilibrium measureexternal fieldRiesz energyminimal energy configurations

Mathematics Subject Classification ID

Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items (2)

A vector equilibrium problem for symmetrically located point charges on a sphere ⋮ Logarithmic equilibrium on the sphere in the presence of multiple point charges

Uses Software

• L-BFGS-B
• L-BFGS
• DLMF
• LBFGS-B

Cites Work

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• Multiscale approximation for functions in arbitrary Sobolev spaces by scaled radial basis functions on the unit sphere
• Multiscale RBF collocation for solving PDEs on spheres
• Riesz external field problems on the hypersphere and optimal point separation
• Weighted energy problem on the unit sphere
• Riesz spherical potentials with external fields and minimal energy points separation
• Riesz extremal measures on the sphere for axis-supported external fields
• Where does the sup norm of a weighted polynomial live? (A generalization of incomplete polynomials)
• Harmonic properties of the logarithmic potential and the computability of elliptic Fekete points
• A facility location formulation for stable polynomials and elliptic Fekete points
• Algorithm 778: L-BFGS-B
• Equilibrium Potentials with External Fields

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