Special problems

Some applications combine operators and boundary conditions representing phenomena that admit various forms of irregularities. In two-point boundary value problems one generally works with weak solutions, but there are also problems of a special character: singular problems and singular perturbation problems. In 2D and 3D problems, singularities may also occur due to the computational domain having a nonsmooth boundary, e.g. with corners. Here we shall only consider 1D, showing examples of how the previous theory is affected, and that singular operators, too, have logarithmic norms.