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Lattices with finite
renormalized coulombian interaction energy in the plane
Yuxin Ge and Etienne Sandier |
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Vol. 3 (2021), No. 1, 93–120
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Abstract |
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We present criteria for a certain coulombian interaction energy of infinitely many points in , , with a uniformly charged background, to be finite, as well as examples. We also show that in this unbounded setting, it is not always possible to project an vector field onto the set of gradients in a way that reduces its average norm on large balls. |
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Keywords
coulombian renormalized energy, Fekete points, jellium,
quasiperiodic lattices
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Mathematical Subject Classification 2010
Primary: 58E20
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Milestones
Received: 20 June 2017
Revised: 25 September 2019
Accepted: 10 October 2019
Published: 29 July 2020
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Authors |
| Yuxin Ge | |
| Institut de Mathématiques de
Toulouse Université Paul Sabatier Toulouse France |
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| Etienne Sandier | |
| Laboratoire d’Analyse et de
Mathématiques Appliquées CNRS UMR 8050 Département de Mathématiques Université Paris Est-Créteil Val de Marne Créteil France |
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