On a 3D-hypersingular equation of a problem for a crack

Samko, Stefan

http://hdl.handle.net/10400.1/11661

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Authors

Samko, Stefan

Abstract(s)

We show that a certain axisymmetric hypersingular integral equation arising in problems of cracks in the elasticity theory may be explicitly solved in the case where the crack occupies a plane circle. We give three different forms of the resolving formula. Two of them involve regular kernels, while the third one involves a singular kernel, but requires less regularity assumptions on the the right-hand side of the equation.