We prove integral formulations of the eikonal equation , 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 , the front has locally finite perimeter in , 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. 253–283DOI 10.4171/IFB/164