# Akseli Haaralas: On the electrostatic Born-Infeld equations and the Lorentz mean curvature operator

**Time: **
Wed 2019-11-13 13.15 - 14.14

**Lecturer: **
Akseli Haaralas, Helsingin yliopisto (University of Helsinki)

**Location: **
KTH, room F11

### Abstract

In 1930's Born and Infeld proposed a new model of nonlinear electrodynamics. In the electrostatic case the Born-Infeld equations lead to the study of a certain quasilinear, non-uniformly elliptic operator that comes with a natural gradient constraint. The same operator appears also as the mean curvature operator of spacelike surfaces in the Lorentz-Minkowski space, the setting of special relativity. We will explain both of these contexts to motivate the mathematical study of said operator.

Our main focus will be on the regularity of the solutions of the electrostatic Born-Infeld equations. We will talk about some now classical results as well as some recent developments. We hope to give some ideas on the problems and methods involved without going into details.