Local Calibrations for Minimizers of the Mumford-shah Functional with a Triple Junction
نویسنده
چکیده
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 ∂U . The proof is obtained by using the calibration method. Mathematics Subject Classification: 49K10 (49Q20).
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