Abstract
The validity of singular integral equations (with Cauchy type kernels) of the first kind and with index equal to 1 at the end-points of the integration interval is shown under mild continuity assumptions. The singular integral.becomes now a divergent integral and has to be interpreted as a finite-part integral. This result is applicable to crack problems in elasticity theory and to the methods for the numerical solution of singular integral equations. As an application, the “natural” extrapolation formula for the determination of the stress intensity factors at the crack tips is obtained. The generalization of the present results to the case of singular integral equations of the second kind is also considered.
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