Stable regular critical points of the Mumford–Shah functional are local minimizers
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 3, p. 533-570
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In this paper it is shown that any regular critical point of the Mumford–Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the L 1 -topology. A global minimality result in small tubular neighborhoods of the discontinuity set is also established.

DOI : https://doi.org/10.1016/j.anihpc.2014.01.006
Classification:  49K10,  49Q20
Keywords: Mumford–Shah functional, Free discontinuity problems, Second variation
@article{AIHPC_2015__32_3_533_0,
     author = {Bonacini, M. and Morini, M.},
     title = {Stable regular critical points of the Mumford--Shah functional are local minimizers},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {32},
     number = {3},
     year = {2015},
     pages = {533-570},
     doi = {10.1016/j.anihpc.2014.01.006},
     zbl = {1316.49026},
     mrnumber = {3353700},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2015__32_3_533_0}
}
Bonacini, M.; Morini, M. Stable regular critical points of the Mumford–Shah functional are local minimizers. Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 3, pp. 533-570. doi : 10.1016/j.anihpc.2014.01.006. http://www.numdam.org/item/AIHPC_2015__32_3_533_0/

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