The Weierstrass–Erdmann condition is a mathematical result from the

calculus of variations The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

, 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

y(x)

of a

functional Functional may refer to: * Movements in architecture: ** Functionalism (architecture) ** Form follows function * Functional group, combination of atoms within molecules * Medical conditions without currently visible organic basis: ** Functional s ...

J=\int\limits_a^b f(x,y,y')\,dx

satisfies the following two continuity relations at each corner

c\in,b /math>:

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

{{DEFAULTSORT:Weierstrass-Erdmann Condition Calculus of variations