# Integral formulations of the geometric eikonal equation

### Aurélien Monteillet

Université de Bretagne Occidentale, Brest, France

## Abstract

We prove integral formulations of the eikonal equation $u_{t}=c(x,t)∣Du∣$, equivalent to the notion of viscosity solution in the framework of the set-theoretic approach to front propagation problems. We apply these integral formulations to investigate the regularity of the front: we prove that under regularity assumptions on the velocity $c$, the front has locally finite perimeter in ${c=0}$, and we give a time-integral estimate of its perimeter.

## Cite this article

Aurélien Monteillet, Integral formulations of the geometric eikonal equation. Interfaces Free Bound. 9 (2007), no. 2, pp. 253–283

DOI 10.4171/IFB/164