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 known that such an approach works in an L2-framework. This book deals with the question of whether it is possible to derive a corresponding Lp-theory for p not equal to 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 ...
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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 known that such an approach works in an L2-framework. This book deals with the question of whether it is possible to derive a corresponding Lp-theory for p not equal to 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 related to the Stokes system with resolvent term. 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 is considered. The proof of the corresponding results is worked out in detail so that the book should be accessible not only to scientists working in the field, but also to graduate students.
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