  We prove that, if u is a function satisfying all Euler conditions for the
Mumford-Shah functional and the discontinuity set of u is given by three line
segments meeting at the origin with equal angles, then there exists a
neighbourhood U of the origin such that u is a minimizer of the Mumford-Shah
functional on U with respect to its own boundary conditions on the boundary of
U. The proof is obtained by using the calibration method.

Functional Analysis