Abstract - We show Euler equations fulfilled by strong minimizers of Blake and Zisserman functional. We prove an Almansi-type decomposition and provide explicit coefficients of asymptotic expansion for bi-harmonic functions in a disk with a cut from center to boundary. We deduce the stress intensity factor and modes coefficients of the leading term in the expansion around crack-tip for any locally minimizing triplet of the main part of Blake and Zisserman functional in the strong formulation. We exhibit explicitly a non-trivial candidate for minimality which has a crack-tip and fulfills all integral and geometric conditions of extremality.

A candidate local minimizer of Blake and Zisserman functional

TOMARELLI, FRANCO
2011

Abstract

Abstract - We show Euler equations fulfilled by strong minimizers of Blake and Zisserman functional. We prove an Almansi-type decomposition and provide explicit coefficients of asymptotic expansion for bi-harmonic functions in a disk with a cut from center to boundary. We deduce the stress intensity factor and modes coefficients of the leading term in the expansion around crack-tip for any locally minimizing triplet of the main part of Blake and Zisserman functional in the strong formulation. We exhibit explicitly a non-trivial candidate for minimality which has a crack-tip and fulfills all integral and geometric conditions of extremality.
Calculus of variations; Free discontinuity; Necessary conditions for local minimizer; Image segmentation
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/577918
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