Between Maxwell and Born-Infeld: the presence of the magnetic field

2024/03/13 by Pietro d’Avenia, d'Avenia, Pietro, Jarosław Mederski +1
Biochemistry, Genetics and Molecular Biology · #35J93 #35Q60 #78A30 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geomagnetism and Paleomagnetism Studies #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2403.08924

openalex publication_date 2024/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Our motivation is to consider an electromagnetic Lagrangian density L_q, depending on a parameter such that, for q=1 it corresponds to the Born-Infeld Lagrangian density and for q=2 it restores the Maxwell one. The model in the presence of given charge and current densities is investigated. We solve the pure magnetostatic problem for q∈(6/5,2). We also study the electrostatic problem in the presence of an assigned magnetic field for q∈[1,2).

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