Existence of extreme crack shapes

Consider the problem of finding the extreme crack shapes. The setting of this problem is as follows. Let C be a convex, closed and 

The problem of finding an extreme crack shape is formulated as follows  

In what follows we prove the existence of the extreme crack shape. 

Theorem 4.8. Let the above hypotheses be fulfilled. Then there exists a solution of the problem (4.177). 

Denote by -0 G the elements of a minimizing sequence. Without decreasing a generality we assume that as n — oo 

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In the following we analyse the behaviour of the solution as 5 —> 0. It will enable us in the sequel to prove the existence of extreme crack shapes. The formulation of this problem is given below. So, for every fixed 5 there exists a solution = iyV of the problem... 

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