TY - JOUR
T1 - Stable regular critical points of the Mumford-Shah functional are local minimizers
JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis
Y1 - 2015
A1 - Marco Bonacini
A1 - Massimiliano Morini
KW - Mumford-Shah functional
AB - In this paper it is shown that any regular critical point of the Mumfordâ€“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.

PB - SISSA
VL - 32
UR - https://www.sciencedirect.com/science/article/pii/S0294144914000171
IS - 3
U1 - 6992
U2 - Mathematics
U4 - 1
U5 - MAT/05 ANALISI MATEMATICA
ER -
TY - JOUR
T1 - A second order minimality condition for the Mumford-Shah functional
JF - Calc. Var. Partial Differential Equations 33 (2008) 37-74
Y1 - 2008
A1 - Filippo Cagnetti
A1 - Maria Giovanna Mora
A1 - Massimiliano Morini
AB - 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.
UR - http://hdl.handle.net/1963/1955
U1 - 2318
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Surfactants in Foam Stability: A Phase-Field Model
JF - Arch. Rational Mech. Anal. 183 (2007) 411-456
Y1 - 2007
A1 - Irene Fonseca
A1 - Massimiliano Morini
A1 - Valeriy Slastikov
AB - The role of surfactants in stabilizing the formation of bubbles in foams is studied using a phase-field model. The analysis is centered on a van der Walls-Cahn-Hilliard-type energy with an added term accounting for the interplay between the presence of a surfactant density and the creation of interfaces. In particular, it is concluded that the surfactant segregates to the interfaces, and that the prescriptionof the distribution of surfactant will dictate the locus of interfaces, what is in agreement with experimentation.
UR - http://hdl.handle.net/1963/2035
U1 - 2161
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Sequences of Singularly Perturbed Functionals Generating Free-Discontinuity Problems
JF - SIAM J. Math. Anal. 35 (2003) 759-805
Y1 - 2003
A1 - Massimiliano Morini
AB - We prove that a wide class of singularly perturbed functionals generates as $\\\\Gamma$-limit a functional related to a free-discontinuity problem. Several applications of the result are shown.
PB - SIAM
UR - http://hdl.handle.net/1963/3071
U1 - 1262
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -