##### Sesión Ecuaciones Diferenciales y Probabilidad

Diciembre 15, 12:00 ~ 12:20

## Regularity for the Far Field Refractor

### Tournier, Federico

In this paper we prove $C^{1}$ regularity for generalized solutions of the far field refractor problem. We consider both the cases $\kappa>1$ and $\kappa<1$ which lead to different geometric constructions. We assume that the domain and target sets are reciprocally convex subsets of the unit sphere under the natural definition of convexity. We also assume bounded densities. The method of proof relies on comparing the ellipsoids of minimum volume containing the proyected sections with the image of the normal mapping of the section.

Autores: Tournier, Federico / Gutierrez, Cristian.