Geodesic
On a 3D-Hypersingular Equation of a Problem for a Crack
Fractional calculus and applied analysis, Tome 14 (2011) no. 1, pp. 19-30.

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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.
Keywords: Fractional Operator, Hypersingular Integrals, Diffraction, Cracks, Potential Kernel, Singular Operator 
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Samko, Stefan. On a 3D-Hypersingular Equation of a Problem for a Crack. Fractional calculus and applied analysis, Tome 14 (2011) no. 1, pp. 19-30. http://geodesic.mathdoc.fr/item/FCAA_2011_14_1_a1/