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25 April 2024

» arxiv » math.FA/0006073

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Local calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets
Gianni Dal Maso ; Maria Giovanna Mora ; Massimiliano Morini ;
Date:	9 Jun 2000
Journal:	J. Math. Pures Appl. 79, 2 (2000) 141-162
Subject:	Functional Analysis \| math.FA
Abstract:	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 $partial U$.
Source:	arXiv, math.FA/0006073
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