Pseudodifferential operators of order minus one

Weakly singular integral operators arise, for example, in the approximation of the solution of elliptic boundary value problems by the so–called boundary element method. In this section we shall consider pseudodifferential operators of order minus one which give rise to coercive quadratic forms on H ^−1/2(Ω) (to be defined). The aforementioned integral operators will be our main example. We shall develop multigrid algorithms for solving the associated discrete equations.