TITLE

A second order minimality condition for the Mumford-Shah functional

AUTHOR(S)
Cagnetti, F.; Mora, M.; Morini, M.
PUB. DATE
September 2008
SOURCE
Calculus of Variations & Partial Differential Equations;Sep2008, Vol. 33 Issue 1, p37
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on H 10( G), G being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of G. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.
ACCESSION #
32562684

 

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