Lorentz space estimates for the Coulombian renormalized energy

Details Lorentz space estimates for the Coulombian renormalized energy Lorentz space estimates for the Coulombian renormalized energy

2011-05-19

arxiv.org/abs/1105.3960v1

Mathematics

Analysis of PDEs

23 pages

Scientific paper

In this paper we obtain optimal estimates for the "currents" associated to
point masses in the plane, in terms of the Coulombian renormalized energy of
Sandier-Serfaty \cite{ss1,ss3}. To derive the estimates, we use a technique
that we introduced in \cite{st}, which couples the "ball construction method"
to estimates in the Lorentz space $L^{2,\infty}$.

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