Integral formulations of the geometric eikonal equation (Q2468803)

Summary: 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 \(\{c\neq 0\}\), and we give a time-integral estimate of its perimeter.