Lorentz space estimates for the Coulombian renormalized energy

2011/05/19 by Sylvia Serfaty, Ian Tice, Serfaty, Sylvia +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1105.3960

23 pages

arxiv created 2011/05/19 · arxiv updated 2011/05/20

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 \citess1,ss3. To derive the estimates, we use a technique that we introduced in \citest, which couples the "ball construction method" to estimates in the Lorentz space L^2,∞.

Related

• Lorentz Space Estimates for the Ginzburg-Landau Energy
• Lorentz Space Estimates and Jacobian Convergence for the Ginzburg-Landau Energy with Applied Magnetic Field
• Lorentz Covariance in Epstein-Glaser Renormalization
• On lattices with finite Coulombian interaction energy in the plane
• Higher Dimensional Coulomb Gases and Renormalized Energy Functionals