Griffith formula and Rice-Cherepanov integral

To underline the dependence of the domain fl on the crack length I we shall write fli instead of fl in some places of this subsection. 

Let be defined by the formula (4.64), and the function 9 be chosen as that at the beginning of Section 4.6.2. Our purpose is to prove the following Griffith formula. 

We have noted that the transformation (4.69) establishes a one-to-one mapping between Kg and Kq, hence 

We first have to prove that the right-hand side of (4.84) does not depend on 9. As we know (see Yakunina, 1981) the solution of the problem (4.62)-(4.63) has an additional regularity up to the crack faces. For any x G Ei there exists a neighbourhood V of the point x such that 

Moreover, the solution u satisfies the following boundary conditions  

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