2000/06/09 by Gianni Dal Maso, Maria Giovanna Mora, Massimiliano Morini
Mathematics · #math.FA
published as J. Math. Pures Appl. 79, 2 (2000) 141-162 · 22 pages, 4 figures
arxiv created 2000/06/09 · arxiv updated 2009/11/30
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.