Lorentz space estimates for the coulombian renormalized energy

Sylvia Serfaty, Ian Tice

Research output: Contribution to journalArticlepeer-review

Abstract

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 [From the GinzburgLandau model to vortex lattice problems, to appear in Comm. Math. Phys. (2012); One-dimensional log gases and the renormalized energy, in preparation]. To derive the estimates, we use a technique that we introduced in [Lorentz space estimates for the Ginzburg-Landau energy, J. Funct. Anal. 254(3) (2008) 773-825], which couples the "ball construction method" to estimates in the Lorentz space L 2,∞.

Original languageEnglish (US)
Article number1250027
JournalCommunications in Contemporary Mathematics
Volume14
Issue number4
DOIs
StatePublished - Aug 2012

Keywords

  • Coulomb gas
  • Ginzburg-Landau
  • Lorentz space
  • Renormalized energy
  • ball construction

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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