平面上具有有限重整化库仑相互作用能的格

IF 0.8 Q2 MATHEMATICS Tunisian Journal of Mathematics Pub Date : 2021-01-01 DOI:10.2140/tunis.2021.3.93

Yuxin Ge, E. Sandier

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引用次数: 1

摘要

。我们提出了[5]中引入的具有均匀带电背景的平面中无限多个点的库仑相互作用能的标准，以及例子。我们还表明，在这种无界设置中，不可能总是以降低其在大球上的平均L2范数的方式将L2向量场投影到梯度集上。

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Lattices with finite renormalized coulombian interaction energy in the plane

. We present criteria for the coulombian interaction energy of inﬁnitely many points in the plane with a uniformly charged background introduced in [5] to be ﬁnite, as well as examples. We also show that in this unbounded setting, it is not always possible to project an L 2loc vector ﬁeld onto the set of gradients in a way that reduces its average L 2 norm on large balls.

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