A new variant of the subdomain method for integral equations of the third kind with singularities in the kernel (Q647869)

The authors study integral equations of the third kind with fixed singularities in the kernel. The integral is understood in the sense of the Hadamard finite part. They construct a new variant of the subdomain method for the approximate solution in the space of generalized functions. They prove the unique solvability of the corresponding approximate equation, estimate the error of the approximate solution and prove the convergence of a sequence of approximate solutions to the exact one. The stability and well-posedness of the approximating equations are also studied.