Hypersingular integral equations and their applications - ISBN:0415309980

Hypersingular integral equations and their applications

Date: 14 April 2011, 11:38

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Hypersingular integral equations, i.e., integral equations whose kernel has a singularity of an order greater than one, are a convenient tool for studying spatial problems in air and fluid dynamics, elasticity, the theory of diffraction of electromagnetic and acoustic waves, ecology, etc. Usually, hypersingular integral equations are obtained as a result of reducing Neumann boundary value problems for the Laplace or the Helmholtz equation to integral equations by means of the double- layer potential. In this book, exact analytical solutions of some two-dimensional hypersingular integral equa- equations are constructed for the first time. An analytical solution in quadratures is obtained for the hypersingular equation on the sphere to which the Neumann problem for the Laplace equation on the sphere is reduced. The book also contains an original exposition of some topics in the theory of the double-layer and single-layer potentials.

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