# $C^{1,\alpha}$-estimates for the near field refractor

## TL;DR

This paper proves local $C^{1,eta}$ regularity estimates for near field refractors in geometric optics, under certain structural target assumptions, without requiring smooth densities.

## Contribution

It introduces new $C^{1,eta}$ regularity results for near field refractors with minimal assumptions on densities and target structure.

## Key findings

- Established local $C^{1,eta}$ estimates for near field refractors
- Achieved regularity results without smoothness assumptions on densities
- Provided structural conditions on the target for regularity

## Abstract

We establish local $C^{1,\alpha}$ estimates for one source near field refractors under structural assumptions on the target, and with no assumptions on the smoothness of the densities.