Weierstrass–Erdmann condition
The Weierstrass–Erdmann condition is a mathematical result from the
extremals (that is, an extremal which is constrained to be smooth except at a finite number of "corners").[1]
Conditions
The Weierstrass-Erdmann corner conditions stipulate that a broken extremal of a functional satisfies the following two continuity relations at each corner :
- .
Applications
The condition allows one to prove that a corner exists along a given extremal. As a result, there are many applications to
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
- ISBN 9780486135014.