Browsing by Author "Bonacini, Marco"

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    Stability of equilibrium configurations for elastic films in two and three dimensions
    (SISSA, 2013-08) Bonacini, Marco; Mathematics
    We establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional case and for a general class of nonlinear elastic energies. Applications to the study of the local minimality of flat morphologies are also shown.
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    Stable regular critical points of the Mumford-Shah functional are local minimizers
    (SISSA, 2013-07) Bonacini, Marco; Morini, Massimiliano; Mathematics
    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 L^1-topology.