Eikonal equation

Summary

The eikonal equation $\abs{\nabla u} = f$ says that the gradient of the unknown function has a prescribed length at each point. It is a stationary Hamilton–Jacobi equation. Its solutions measure travel times: with $f = 1$ and $u = 0$ on the boundary of a domain, the viscosity solution is the distance to the boundary. It is the basic equation of geometric optics, where the level sets of $u$ are the wave fronts. See the definition.