@article {2013, title = {Stable regular critical points of the Mumford-Shah functional are local minimizers}, journal = {Annales de l{\textquoteright}Institut Henri Poincare (C) Non Linear Analysis}, volume = {32}, number = {SISSA preprint;SISSA 33/2013/MATE}, year = {2015}, pages = {533-570}, publisher = {SISSA}, chapter = {533}, abstract = {

In this paper it is shown that any regular critical point of the Mumford{\textendash}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.

}, keywords = {Mumford-Shah functional}, doi = {10.1016/j.anihpc.2014.01.006}, url = {https://www.sciencedirect.com/science/article/pii/S0294144914000171}, author = {Marco Bonacini and Massimiliano Morini} } @mastersthesis {2001, title = {Numerical Methods for Free-Discontinuity Problems Based on Approximations by Γ-Convergence}, year = {2001}, school = {SISSA}, keywords = {Mumford-Shah functional}, url = {http://hdl.handle.net/1963/5399}, author = {Matteo Negri} }