Local calibrations for minimizers of the Mumford-Shah functional with a triple junction

We prove that, if u is a function satisfying all the 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 of the origin such that u is a minimizer of the Mumford-Shah functional on this set with respect to its own boundary conditions. The proof is obtained by using the calibration method