Lorentz space estimates for the coulombian renormalized energy

Sylvia Serfaty; Ian Tice

doi:10.1142/S0219199712500277

Lorentz space estimates for the coulombian renormalized energy

Sylvia Serfaty, Ian Tice

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Article number	1250027
Journal	Communications in Contemporary Mathematics
Volume	14
Issue number	4
DOIs	https://doi.org/10.1142/S0219199712500277
State	Published - Aug 2012

Keywords

Coulomb gas
Ginzburg-Landau
Lorentz space
Renormalized energy
ball construction

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1142/S0219199712500277

Cite this

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title = "Lorentz space estimates for the coulombian renormalized energy",

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,∞.",

keywords = "Coulomb gas, Ginzburg-Landau, Lorentz space, Renormalized energy, ball construction",

author = "Sylvia Serfaty and Ian Tice",

note = "Funding Information: The first author was supported by an EURYI Award. The second author was supported by an NSF Postdoctoral Research Fellowship.",

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language = "English (US)",

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AU - Tice, Ian

N1 - Funding Information: The first author was supported by an EURYI Award. The second author was supported by an NSF Postdoctoral Research Fellowship.

PY - 2012/8

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N2 - 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,∞.

AB - 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,∞.

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KW - Renormalized energy

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Lorentz space estimates for the coulombian renormalized energy

Abstract

Keywords

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