  In this paper we study the asymptotic behaviour of the solutions of some
minimization problems for integral functionals with convex integrands, in
two-dimensional domains with cracks, under perturbations of the cracks in the
Hausdorff metric. In the first part of the paper, we examine conditions for the
stability of the minimum problem via duality arguments in convex optimization.
In the second part, we study the limit problem in some special cases when there
is no stability, using the tool of $\Gamma$-convergence.
