Convergent perturbative power series solution of the stationary Maxwell–Born–Infeld field equations with regular sources

摘要

The stationaryMaxwell–Born–Infeld field equations of electromagnetism with regular sources ρ ∈ (C_0~α ∩ L~1)(R~3) and j ∈ (C_0~α ∩ L~1)(R~3) (componentwise) are solved using a perturbation series expansion in powers of Born’s electromagnetic constant. The convergence in C_0~(1,α) of the power series for the fields is proved with the help of Banach algebra arguments and complex analysis. The finite radius of convergence depends on the “C_0~(1,α) size” of both, the Coulomb field generated by ρ and the Ampere field generated by j . No symmetry is assumed.