Kernel Properties and Representations of Boundary Integral Operators

Boundary integral operators arise in the reduction to the boundary method for solving elliptic boundary value problems. These are classical pseudodifferential operators of integer order on the boundary. In order to exploit these boundary integral operators for computational methods one needs explicit knowledge of the corresponding kernel properties in the framework of Hadamard finite part regularization, explicit representation based on local polar coordinates and explicit transformation under the change of the parametric representation of the boundary manifold. Here we present these properties for the special case of a (piecewise) smooth two-dimensional boundary surface immersed into ℝ3.