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

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

2000-06-09

arxiv.org/abs/math/0006073v1

J. Math. Pures Appl. 79, 2 (2000) 141-162

Mathematics

Functional Analysis

22 pages, 4 figures

Scientific paper

Using a calibration method, we prove that, if $w$ is a function which satisfies all Euler conditions for the Mumford-Shah functional on a two-dimensional open set $\Omega$, and the discontinuity set of $w$ is a segment connecting 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 $w$ is a minimizer of the Mumford-Shah functional on $U$ with respect to its own boundary values on $\partial U$.

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