Stable regular critical points of the Mumford–Shah functional are local minimizers
M. Bonacini
SISSA, Via Bonomea 265, 34136 Trieste, ItalyM. Morini
Dipartimento di Matematica, Università degli Studi di Parma, Parma, Italy
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Abstract
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 -topology. A global minimality result in small tubular neighborhoods of the discontinuity set is also established.
Cite this article
M. Bonacini, M. Morini, Stable regular critical points of the Mumford–Shah functional are local minimizers. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 3, pp. 533–570
DOI 10.1016/J.ANIHPC.2014.01.006