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<p>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.</p>

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Function spaces on uniformly regular and singular Riemannian manifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月15日

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  • Herbert Amann

摘要

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.