Born-Infeld corrections to Coulombian interactions
  Two-dimensional Born-Infeld electrostatic fields behaving as the superposition of two point-like charges in the linearized (Maxwellian) limit are worked out by means of a non-holomorphic mapping of the complex plane. The changes underwent by the Coulombian interaction between two charges in Born-Infeld theory are computed. Remarkably, the force between equal charges goes to zero as they approach each other. 
Rafael Ferraro, Maria Evangelina Lipchak