Anisotropic Function Spaces on Singular Manifolds

Abstract

A rather complete investigation of anisotropic Bessel potential, Besov, and Hölder 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.

96 pages

References in corpus (2)

• Pointwise multiplication of Besov and Triebel--Lizorkin spaces
• Bounded ${\mathbf{H}}_{\infty }$-Calculus for Differential Operators on Conic Manifolds with Boundary

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• On the flow of non-axisymmetric perturbations of cylinders via surface diffusion
• Global solutions to the Porous medium equations on singular manifolds
• Anisotropic regularity and optimal rates of convergence for the Finite Element Method on three dimensional polyhedral domains