Geodesic
Convex Representation for Lower Semicontinuous Envelopes of Functionals in L1
Journal of convex analysis, Tome 8 (2001) no. 1, pp. 149-17
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G. Alberti, G. Bouchitte and G. Dal Maso [The calibration method for the Mumford-Shah functional, C. R. Acad. Sci. Paris 329, Serie I (1999) 249--254] recently found sufficient conditions for the minimizers of the (nonconvex) Mumford-Shah functional. Their method consists in an extension of the calibration method (that is used for the characterization of minimal surfaces), adapted to this functional. The existence of a calibration, given a minimizer of the functional, remains an open problem. 
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     author = {A. Chambolle},
     title = {Convex {Representation} for {Lower} {Semicontinuous} {Envelopes} of {Functionals} in {L\protect\textsuperscript{1}}},
     journal = {Journal of convex analysis},
     pages = {149--17},
     year = {2001},
     volume = {8},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2001_8_1_JCA_2001_8_1_a6/}
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A. Chambolle. Convex Representation for Lower Semicontinuous Envelopes of Functionals in L1. Journal of convex analysis, Tome 8 (2001) no. 1, pp. 149-17. http://geodesic.mathdoc.fr/item/JCA_2001_8_1_JCA_2001_8_1_a6/