Vol. 3, No. 1, 2021

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Lattices with finite renormalized coulombian interaction energy in the plane

Yuxin Ge and Etienne Sandier

Vol. 3 (2021), No. 1, 93–120
Abstract

We present criteria for a certain coulombian interaction energy of infinitely many points in d, d 1, 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 Lloc2 vector field onto the set of gradients in a way that reduces its average L2 norm on large balls.

Keywords
coulombian renormalized energy, Fekete points, jellium, quasiperiodic lattices
Mathematical Subject Classification 2010
Primary: 58E20
Milestones
Received: 20 June 2017
Revised: 25 September 2019
Accepted: 10 October 2019
Published: 29 July 2020
Authors
Yuxin Ge
Institut de Mathématiques de Toulouse
Université Paul Sabatier
Toulouse
France
Etienne Sandier
Laboratoire d’Analyse et de Mathématiques Appliquées
CNRS UMR 8050
Département de Mathématiques
Université Paris Est-Créteil Val de Marne
Créteil
France