On the electrostatic Born-Infeld equation with point charges

In this seminar I will present some results on the electrostatic Born-Infeld equation set in the whole R^n. This equation is governed by the Lorentz-Minkowski mean curvature operator and was introduced, in the theory of nonlinear electromagnetism, as a generalization of the Poisson equation for the electrostatic potential. I will consider the case of a superposition of (possibly non-symmetrically distributed) point charges and discuss sufficient conditions to guarantee that the minimizer of the action functional is a solution of the problem. I will also present an approximation of the considered problem, governed by a sum of 2m-Laplacians, and show some qualitative properties of the approximating solutions, such as their behavior near the charges. This is a joint work with Denis Bonheure (Université Libre de Bruxelles) and Juraj Foldes (University of Virginia) available at arXiv:1707.07517.