Local calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets

Using a calibration method, we prove that, if omega is a function which sat isfies all Euler conditions for the Mumford-Shah functional on a two-dimens ional open set Omega, and the discontinuity set of omega is a segment conne cting two boundary points, then for every point (x(0), y(0)) of Omega there exists a neighbourhood U of (x(0), y(0)) such that omega is a minimizer of the Mumford-Shah functional on U with respect to its own boundary values o n partial derivative U. (C) 2000 Editions scientifiques et medicales Elsevi er SAS AMS classification: 49K10 (primary), 49Q20 (secondary).