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

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 Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilin ...

. 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