Integral formulations of the geometric eikonal equation

  • Aurélien Monteillet

    Université de Bretagne Occidentale, Brest, France


We prove integral formulations of the eikonal equation ut=c(x,t)Duu_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 cc, the front has locally finite perimeter in {c0}\{c \neq 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