# On a 3D-Hypersingular Equation of a Problem for a Crack

Fractional Calculus and Applied Analysis (2011)

- Volume: 14, Issue: 1, page 19-30
- ISSN: 1311-0454

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topSamko, Stefan. "On a 3D-Hypersingular Equation of a Problem for a Crack." Fractional Calculus and Applied Analysis 14.1 (2011): 19-30. <http://eudml.org/doc/219572>.

@article{Samko2011,

abstract = {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.},

author = {Samko, Stefan},

journal = {Fractional Calculus and Applied Analysis},

keywords = {Fractional Operator; Hypersingular Integrals; Diffraction; Cracks; Potential Kernel; Singular Operator; fractional operator; hypersingular integrals; diffraction},

language = {eng},

number = {1},

pages = {19-30},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {On a 3D-Hypersingular Equation of a Problem for a Crack},

url = {http://eudml.org/doc/219572},

volume = {14},

year = {2011},

}

TY - JOUR

AU - Samko, Stefan

TI - On a 3D-Hypersingular Equation of a Problem for a Crack

JO - Fractional Calculus and Applied Analysis

PY - 2011

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 14

IS - 1

SP - 19

EP - 30

AB - 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.

LA - eng

KW - Fractional Operator; Hypersingular Integrals; Diffraction; Cracks; Potential Kernel; Singular Operator; fractional operator; hypersingular integrals; diffraction

UR - http://eudml.org/doc/219572

ER -

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