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Higher integrability of the gradient and dimension of the singular set for minimisers of the Mumford–Shah functional

✍ Scribed by Luigi Ambrosio; Nicola Fusco; John E. Hutchinson

Publisher
Springer
Year
2003
Tongue
English
Weight
303 KB
Volume
16
Category
Article
ISSN
0944-2669

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📜 SIMILAR VOLUMES

Local calibrations for minimizers of the
Local calibrations for minimizers of the Mumford–Shah functional with a regular discontinuity set
✍ Maria Giovanna Mora; Massimiliano Morini 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 360 KB

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

Finite difference approximation of the M
Finite difference approximation of the Mumford-Shah functional
✍ Massimo Gobbino 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 333 KB

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