Global calibrations for the non-homogeneous Mumford-Shah functional
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 3, pp. 603-648.

Using a calibration method we prove that, if ΓΩ is a closed regular hypersurface and if the function g is discontinuous along Γ and regular outside, then the function u β which solves

Δu β =β(u β -g)inΩΓ ν u β =0onΩΓ
is in turn discontinuous along Γ and it is the unique absolute minimizer of the non-homogeneous Mumford-Shah functional
ΩS u |u| 2 dx+ n-1 (S u )+β ΩS u (u-g) 2 dx,
over SBV(Ω), for β large enough. Applications of the result to the study of the gradient flow by the method of minimizing movements are shown.

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     title = {Global calibrations for the non-homogeneous {Mumford-Shah} functional},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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Morini, Massimiliano. Global calibrations for the non-homogeneous Mumford-Shah functional. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 3, pp. 603-648. http://archive.numdam.org/item/ASNSP_2002_5_1_3_603_0/

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