A standard argument shows that the solution to (1) is written as

where **G** is the fundamental solution of Laplace's equation given by

and is the crack opening displacement defined by

The unknown functions ** u ** on and on **S**
are determined as the solutions to the following integral equations:

where the integration symbol with a superimposed **=** on the RHS of
(4) stands for the finite part. As
a matter of fact the hypersingular integral equation in (4)
is obtained as one computes the normal derivative of (2)
in and takes the limit onto **S**. A simple but rigorous
proof that the limit takes the form in (4) is found for
example in Nishimura & Kobayashi[31].

Thu Feb 19 01:36:51 JST 1998