%0 Journal Article
%J Calc. Var. Partial Differential Equations 33 (2008) 37-74
%D 2008
%T A second order minimality condition for the Mumford-Shah functional
%A Filippo Cagnetti
%A Maria Giovanna Mora
%A Massimiliano Morini
%X 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.
%B Calc. Var. Partial Differential Equations 33 (2008) 37-74
%G en_US
%U http://hdl.handle.net/1963/1955
%1 2318
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-03-02T12:54:00Z\\nNo. of bitstreams: 1\\nCMM.pdf: 358759 bytes, checksum: c414c0080a17971ecba1251a5890b94f (MD5)
%R 10.1007/s00526-007-0152-3