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Candidate local minimizer of Blake & Zisserman functional
No full textQDD 10, Quaderni digitali del Dipartimento di Matematica del Politecnico di Milano.
http://www.mate.polimi.it/biblioteca/qddview.php?id=1318&L=i
ABSTRACT - Almansi decomposition and explicit coefficients of asymptotic expansion around the origin for bi-harmonic functions in a disk with a crack are evaluated by simbolic computations with Mathematica 5.0 . We deduce S.I.F. and modes coefficients of the leading term in the expansion for candidate local minimizer of Blake & Zisserman functional
Euler equations for Blake & Zisserman functional
No full textWe derive many necessary conditions for minimizers of a functional depending on free discontinuities, free gradient discontinuities and second derivatives, which is related to image segmentation. The necessary conditions are proven by performing several kind of variations
Almansi Decomposition and Expansion of a Polyharmonic Function Near a Crack-Tip
No full textWe study polyharmonic functions in 2-dimensional open sets with a flat crack: for these functions we show a decomposition of Almansi-type and make explicit the coefficients of a strongly converging expansion near the crack-tip
Minimization of the Buckling Load of a Clamped Plate with Perimeter Constraint
Full text linkWe look for minimizers of the buckling load problem with perimeter constraint in any dimension. In dimension 2, we show that the minimizing plates are convex; in higher dimension, by passing through a weaker formulation of the problem, we show that any optimal set is open and connected. For the higher eigenvalues, we prove that minimizers exist among convex sets with prescribed perimeter
Corrigendum to A candidate local minimizer of Blake and Zisserman functional [J. Math. Pures Appl. 96, 1, (2011), 58-87] Doi: 10.1016/j.matpur.2011.01.005
No full textIn a previous paper, focused on the analysis of Blake & Zisserman functional in image segmentation, we showed an Almansi-type decomposition and explicit coefficients of asymptotic expansion for bi-harmonic functions in a disk with a cut from center to boundary. The real form expansions and their subsequent applications are correct, but the auxiliary analysis of complex form expansions is imprecise. Here we wish to make precise this point
A Dirichlet problem with free gradient discontinuity
No full textQuaderni Digitali del Dipartimento di Matematica del Politecnico di Milano, QDD 36. luglio 2008.
Available at http://www.mate.polimi.it/biblioteca/qddview.php?id=1347&L=
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