Primal and Shadow functions, Dual and Dual-Shadow functions for a   circular crack and a circular 90 degree V-notch with Neumann boundary   conditions
  This report presents explicit analytical expressions for the primal, primal shadows, dual and dual shadows functions for the Laplace equation in the vicinity of a circular singular edge with Neumann boundary conditions on the faces that intersect at the singular edge. Two configurations are investigated: a penny-shaped crack and a 90^o V-notch. 
Samuel Shannon, Zohar Yosibash, Monique Dauge (IRMAR), Martin Costabel   (IRMAR)
math.NA