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Numerical minimization¶of the Mumford–Shah functional

✍ Scribed by M. Negri; M. Paolini

Publisher
Springer Milan
Year
2001
Tongue
English
Weight
229 KB
Volume
38
Category
Article
ISSN
0008-0624

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We study the pointwise convergence and the Γ-convergence of a family of nonlocal functionals defined in L 1 loc (R n ) to a local functional F (u) that depends on the gradient of u and on the set of discontinuity points of u. We apply this result to approximate a minimum problem introduced by Mumfor

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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 , and the discontinuity set S w of w is a regular curve connecting two boundary points, then there exists a uniform neighbourhood U of S w