Abstract
Fundamental solutions of the differential operators for the potential problem and the elastostatic problem are established. They are not defined on the ordinary three-dimensional space as the classical 1/R solution and Kelvin's solution but on Riemann spaces with circular branch lines and a finite as well as an infinite number of sheets. The solutions can be used as the kernels of boundary integral equations. Equations of this type should be useful for the determination of displacements and stresses in elastic bodies with slits and cracks of certain shapes.
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