@article {2008,
title = {A second order minimality condition for the Mumford-Shah functional},
journal = {Calc. Var. Partial Differential Equations 33 (2008) 37-74},
number = {SISSA;82/2006/M},
year = {2008},
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 $H^1_0(\\\\Gamma)$, $\\\\Gamma$ 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 $\\\\Gamma$. 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.},
doi = {10.1007/s00526-007-0152-3},
url = {http://hdl.handle.net/1963/1955},
author = {Filippo Cagnetti and Maria Giovanna Mora and Massimiliano Morini}
}