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This report presents explicit analytical expressions for the primal, primalshadows, dual and dual shadows functions for the Laplace equation in thevicinity of a circular singular edge with Neumann boundary conditions on thefaces that intersect at the singular edge. Two configurations are investigated:a penny-shaped crack and a 90^o V-notch.

Primal and Shadow functions, Dual and Dual-Shadow functions for a circular crack and a circular 90 degree V-notch with Neumann boundary conditions