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Function Spaces on Singular Manifolds Math. Institut, Universitat Zurich, Winterthurerstr. 190, CH8057 Zurich, Switzerland

Summary: Function Spaces on Singular Manifolds
H. Amann
Math. Institut, Universit¨at Z¨urich, Winterthurerstr. 190, CH­8057 Z¨urich, Switzerland
Key words Weighted Sobolev spaces, Bessel potential spaces, Besov spaces, singularities, non-complete Rie-
mannian manifolds with boundary
MSC (2000) 46E35, 54C35, 58A99, 58D99
It is shown that most of the well-known basic results for Sobolev-Slobodeckii and Bessel potential spaces,
known to hold on bounded smooth domains in Rn
, continue to be valid on a wide class of Riemannian manifolds
with singularities and boundary, provided suitable weights, which reflect the nature of the singularities, are
introduced. These results are of importance for the study of partial differential equations on piece-wise smooth
1 Introduction
It is our principal concern in this paper to develop a satisfactory theory of spaces of functions and tensor fields on
Riemannian manifolds which may have a boundary and may be non-compact and non-complete. Such a theory
has to extend the basic results known for function spaces on subdomains of Rn
with smooth boundary to this more
general setting, that is to say, embedding and interpolation properties, point-wise multiplier and trace theorems,
duality characterizations and, last but not least, intrinsic local descriptions.
Our research is motivated by -- and provides the basis for -- the study of elliptic and parabolic boundary value


Source: Amann, Herbert - Institut für Mathematik, Universität Zürich


Collections: Mathematics