Calculus of Variations and Geometric Measure Theory

M. Carriero - A. Leaci - F. Tomarelli

A candidate local minimizer of Blake & Zisserman functional

created by tomarelli on 23 Dec 2008
modified on 08 Feb 2013


Published Paper

Inserted: 23 dec 2008
Last Updated: 8 feb 2013

Journal: J. Math. Pures Appl.
Volume: 96
Pages: 58-87
Year: 2011
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