On a 3D-Hypersingular Equation of a Problem for a Crack
Fractional Calculus and Applied Analysis, Tome 14 (2011) no. 1, p. 19.

Voir la notice de l'article dans European Digital Mathematics Library

MSC 2010: 45DB05, 45E05, 78A45We 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.
Classification : 74G05, 78A45, 74R10, 45E05
Mots-clés : Fractional Operator, Hypersingular Integrals, Diffraction, Cracks, Potential Kernel, Singular Operator, fractional operator, hypersingular integrals, diffraction 
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     author = {Samko, Stefan},
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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, p. 19. https://geodesic-test.mathdoc.fr/item/FCAA_2011__14_1_219572/