Function Spaces on Uniformly Regular and Singular Riemannian Manifolds

Abstract

This paper shows that the basic properties of Sobolev, Besov, and Bessel potential spaces are valid on Riemannian manifolds with boundary, which either have bounded geometry or posses singularities. In the latter case the appropriate setting is that of Kondratiev-type weighted spaces. The importance and usefulness of our results are indicated by a demonstration of a maximal regularity result for a linear parabolic initial value problem on singular manifolds.

References in corpus (7)

• Uniform Shapiro-Lopatinski conditions and boundary value problems on manifolds with bounded geometry
• Singular parabolic equations of second order on manifolds with singularities
• The Yamabe flow on incomplete manifolds
• Bounded $H_{\infty }$-calculus for cone differential operators
• Cauchy Problems for Parabolic Equations in Sobolev-Slobodeckii and Hölder Spaces on Uniformly Regular Riemannian Manifolds
• Maximal Regularity of Parabolic Transmission Problems
• On the flow of non-axisymmetric perturbations of cylinders via surface diffusion