Local calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets
نویسندگان
چکیده
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 Ω, and the discontinuity set of w is a segment connecting two boundary points, then for every point (x0, y0) of Ω there exists a neighbourhood U of (x0, y0) such that w is a minimizer of the Mumford-Shah functional on U with respect to its own boundary values on ∂U . AMS (MOS) subject classifications: 49K10 (primary), 49Q20 (secondary)
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