Inserted: 23 dec 2008
Last Updated: 8 feb 2013
Journal: J. Math. Pures Appl.
Links: published online
We show Euler equations fulfilled by strong minimizers of Blake & 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 & Zisserman functional in the strong formulation. We exhibit explicitly a nontrivial candidate for minimality which has a crack-tip and fulfills all integral and geometric conditions of extremality.
Keywords: calculus of variations, free discontinuity, Image segmentation, necessary conditions for local minimizer