Function Spaces on Singular Manifolds

Details Function Spaces on Singular Manifolds Function Spaces on Singular Manifolds

2011-06-10

arxiv.org/abs/1106.2033v5

Mathematics

Functional Analysis

37 pages, 1 figure, final version, augmented by additional references; to appear in Math. Nachrichten

Scientific paper

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 $\mathbb{R}^n$, 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 domains.

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