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

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

2001-05-08

arxiv.org/abs/math/0105057v2

Mathematics

Functional Analysis

28 pages, 4 figures

Scientific paper

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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