# Weierstrass–Erdmann condition

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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.

## 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 , the partial derivative 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.

## 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.