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

TL;DR

This paper develops a convergent perturbative power series method to solve the stationary Maxwell-Born-Infeld equations with regular sources, proving convergence using advanced mathematical techniques without assuming symmetry.

Contribution

It introduces a novel convergent perturbation series approach for Maxwell-Born-Infeld equations with regular sources, extending previous methods by proving convergence in a general setting.

Findings

Power series converges within a finite radius depending on source norms.

Convergence proof uses Banach algebra and complex analysis techniques.

No symmetry assumptions are required for the solution.

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.