Using a calibration method, we prove that, if w is a function which satisfies all the 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 in Omega there exists a neighbourhood U of the point such that w is a minimizer of the Mumford–Shah functional on U with respect to its own boundary values.

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

Mora, M. G.;
2000-01-01

Abstract

Using a calibration method, we prove that, if w is a function which satisfies all the 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 in Omega there exists a neighbourhood U of the point such that w is a minimizer of the Mumford–Shah functional on U with respect to its own boundary values.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/363564
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