Mirrors, lenses and Monge–Ampère equations

Abstract

Is it possible to shape a piece of glass so that it refracts and concentrates sunlight in order to produce a given image? The modelling of this kind of problem leads to nonlinear second-order partial differential equations, which belong to the family of Monge–Ampère equations. We will see how semi-discrete methods, that can be traced back to Minkowski’s works, allow us to numerically solve such equations.