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

Abstract

The stationary Maxwell-Born-Infeld field equations of electromagnetism with integrable regular sources in a Hoelder space are solved using a perturbation series expansion in powers of Born's electromagnetic constant. The convergence 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 norm of both, the Coulombfield generated by the charge density and the Amp`ere field generated by the current density. No symmetry is assumed.