Sobolev Theorems for Cusp Manifolds

  • Jürgen Eichhorn

    Universität Greifswald, Germany
  • Chunpeng Wang

    Jilin University, Changchun, China


In the past, we established a module structure theorem for Sobolev spaces on open manifolds with bounded curvature and positive injectivity radius . The assumption was essential in the proof. But, manifolds with have been excluded. An extension of our former results to the case seems to be hopeless. In this paper, we show that certain Sobolev embedding theorems and a (generalized) module structure theorem are valid in weighted spaces with the weight or .

Cite this article

Jürgen Eichhorn, Chunpeng Wang, Sobolev Theorems for Cusp Manifolds. Z. Anal. Anwend. 32 (2013), no. 4, pp. 389–409

DOI 10.4171/ZAA/1491