Anisotropic Function Spaces on Singular Manifolds

Details Anisotropic Function Spaces on Singular Manifolds Anisotropic Function Spaces on Singular Manifolds

2012-04-03

arxiv.org/abs/1204.0606v1

Mathematics

Functional Analysis

96 pages

Scientific paper

A rather complete investigation of anisotropic Bessel potential, Besov, and H\"older spaces on cylinders over (possibly) noncompact Riemannian manifolds with boundary is carried out. The geometry of the underlying manifold near its 'ends' is determined by a singularity function which leads naturally to the study of weighted function spaces. Besides of the derivation of Sobolev-type embedding results, sharp trace theorems, point-wise multiplier properties, and interpolation characterizations particular emphasize is put on spaces distinguished by boundary conditions. This work is the fundament for the analysis of time-dependent partial differential equations on singular manifolds.

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