The Weierstrass–Erdmann condition is a mathematical result from the calculus of variations, which specifies sufficient conditions for broken extremals (that is, an extremal which is constrained to be smooth except at a finite number of "corners").
Conditions.
The Weierstrass-Erdmann corner conditions stipulate that a broken extremal formula_1 of a functional formula_2 satisfies the following two continuity relations at each corner formula_3:
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.
References.
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