Cauchy data

For a scalar equation of order $k$, Cauchy data consist of the first $k$ normal jets $u,{\partial }_{N}u,\dots ,{\partial }_N^{k-1}u$ on the initial hypersurface.

These prescribed values define the initial conditions of a Cauchy problem.

The boundary jet through order $m-1$ is the collection of traces ${\partial }^{\alpha }u{|}_{\partial \Omega }$ with $|\alpha |\le m-1$. Vanishing of the whole jet is stronger than vanishing of one derivative. On a smooth hypersurface, zero normal Cauchy derivatives through order $m-1$, together with their tangential derivatives, give a zero full boundary jet.