Double-layer potentials may be used in order to construct strong solutions of the Stokes system on Lipschitz bounded domains, under Dirichlet boundary conditions. It is kwown that such an approach works in an L?-framework. This book deals with the question whether it is possible to derive a corresponding Lp-theory for p = 2. To this end, a special Lipschitz domain is chosen, namely a right circular infinite cone. Then the space of all p-integrable functions on the surface of this cone is considered. Two kinds of double ...
Read More
Double-layer potentials may be used in order to construct strong solutions of the Stokes system on Lipschitz bounded domains, under Dirichlet boundary conditions. It is kwown that such an approach works in an L?-framework. This book deals with the question whether it is possible to derive a corresponding Lp-theory for p = 2. To this end, a special Lipschitz domain is chosen, namely a right circular infinite cone. Then the space of all p-integrable functions on the surface of this cone is considered. Two kinds of double-layer potentials are introduced on this space, one related to the Stokes system, the other one to the Stokes system with resolvent term. It is studied how the Fredholm properties of these potentials depend on p, on the vertex angle of the cone, and - in the second case - on the resolvent parameter. The proof of the corresponding results is worked out in detail so that the book should be accessible not only for scientists working in the field, but also for graduate students.
Read Less
