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

Maria Giovanna Mora
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Abstract

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.

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Maria Giovanna Mora. 2001-05-09. Local calibrations for minimizers of the Mumford-Shah functional with a triple junction. https://arxiv.org/abs/math/0105057

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