The electrostatic Born-Infeld equations with integrable charge densities

2020/06/15 by Akseli Haarala, Haarala, Akseli · 2 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Mathematical Physics Problems #Quantum, superfluid, helium dynamics

paper · pdf · doi:10.48550/arxiv.2006.08208

Abstract

We study the minimizer of the electrostatic Born--Infeld energy ∫_ℝⁿ1-√(1-|D v|²) dx-∫_ℝⁿρv dx, which vanishes at infinity. We show that the minimizer u is strictly spacelike and it is a weak solution to -div((D u)/(√(1-|D u|²)))=ρ, provided that ρ is in the dual space of the solution space and ρ∈ L^p(ℝⁿ), for some p>n≥ 3. Moreover, we have u∈ C^1,α(ℝⁿ) for some α∈ (0,1).

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