Function spaces on singular manifolds

By Herbert Amann. 2011

74 citations recorded by the source corpus.

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 \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb R}^n$\end{document}, 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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/4e7533b4ff0d081c4aeeb3372dfe7ac2aacb69ab

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Mark Veraar
2. M. Meyries
3. J. V. Neerven
4. Lutz Weis

Citations in the corpus

• Sharp embedding results for spaces of smooth functions with power weights (2011, background): “Less is known on vector-valued function spaces with weights (see [4, 28] and references therein).”