The Stokes system in an infinite cone
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Bibliographic Information
The Stokes system in an infinite cone
（Mathematical research = Mathematische Forschung, v. 78）
Akademie Verlag, c1994
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Note
Bibliography: p. [265]-267
Description and Table of Contents
Description
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.
Table of Contents
- A Riesz potential on the surface of an infinite cone
- some elements of the theory of locally compact abelian groups
- applications to the double-layer potential for the Stokes system
- the double-layer potential for the resolvent problem - an Lp theory
- some connections with the L2-theory of the Stokes system on bounded Lipschitz domains. (Part contents).
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