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Weighted energy problem on the unit sphere

Weighted energy problem on the unit sphere We consider the minimal energy problem on the unit sphere $${\mathbb {S}}^2$$ S 2 in the Euclidean space $${\mathbb {R}}^3$$ R 3 immersed in an external field Q, where the charges are assumed to interact via Newtonian potential 1/r, r being the Euclidean distance. The problem is solved by finding the support of the extremal measure, and obtaining an explicit expression for the equilibrium density. We then apply our results to an external field generated by a point charge, and to a quadratic external field. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Weighted energy problem on the unit sphere

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Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer International Publishing
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-016-0125-9
Publisher site
See Article on Publisher Site

Abstract

We consider the minimal energy problem on the unit sphere $${\mathbb {S}}^2$$ S 2 in the Euclidean space $${\mathbb {R}}^3$$ R 3 immersed in an external field Q, where the charges are assumed to interact via Newtonian potential 1/r, r being the Euclidean distance. The problem is solved by finding the support of the extremal measure, and obtaining an explicit expression for the equilibrium density. We then apply our results to an external field generated by a point charge, and to a quadratic external field.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Feb 5, 2016

References