Integral Equations with Hypersingular Kernels -- Theory and Applications to Fracture Mechanics

Youn-Sha Chan, Albert C. Fannjiang, Glaucio H. Paulino

Hypersingular integrals of the type $I_α(T_n,m,r) = \int_{-1}^{1} \hpsngAbs \frac{T_n(s)(1-s^2)^{m-{1/2}}}{(s-r)^α}ds |r|<1$ and $I_α(U_n,m,r) = \int_{-1}^{1} \hpsngAbs \frac{U_n(s…