LOCALLY NICE EMBEDDINGS IN CODIMENSION THREE

ity and t independence of the operator P(xt D). This permits P to be a quite general operator. Finally, if Pi and P2 reduce to initial value problems, a similar argument is applicable. In this case, conditions on the known function u(x, t) (or v(xf t)) can be imposed on the unknown function v(x, t) (or u(x, t)). With no boundary conditions on u and v, it is no longer necessary to require that {x) satisfy a boundary condition.