# Weierstrass–Erdmann condition

The condition says that, along a piecewise smooth extremal x(t) (i.e. an extremal which is smooth except at a finite number of corners) for an integral $J=\int f(t,x,y)\,dt$, the partial derivative $\partial f/\partial x$ must be continuous at a corner T. That is, if one takes the limit of partials on both sides of the corner as one approaches the corner T, the result must be the same answer.