The Weierstrass–Erdmann condition is a technical tool from the calculus of variations. This condition gives the sufficient conditions for an extremal to have a corner.
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Conditions
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
Applications
The condition allows one to prove that a corner exists along a given extremal. As a result, there are many applications to differential geometry. In calculations of the Weierstrass E-Function, it is often helpful to find where corners exist along the curves. Similarly, the condition allows for one to find a minimizing curve for a given integral.