Abstract
We want to justify the operations used when deriving equations, first of all hypersingular equations. What do we need to prove? In our discussion and derivations of hypersingular integrals, we employed the following formal elements:
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a)
we assumed that there is a definition of divergent integrals that endows them with the usual properties of integrals, specifically with linearity and additivity;
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b)
we used differentiation under the integral sign;
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c)
we used integration by parts;
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d)
we used formulae of Sokhotski-Plemelj type that connect direct values of divergent integrals with their limiting values.
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© 2002 Springer Science+Business Media Dordrecht
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Linkov, A.M. (2002). Complex Hypersingular and Finite-Part Integrals. In: Boundary Integral Equations in Elasticity Theory. Solid Mechanics and Its Applications, vol 99. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9914-6_11
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DOI: https://doi.org/10.1007/978-94-015-9914-6_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6000-6
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