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Annals of Global Analysis and Geometry

, Volume 39, Issue 2, pp 107–129 | Cite as

Density of smooth maps in W k, p(M, N) for a close to critical domain dimension

  • Andreas GastelEmail author
  • Andreas J. Nerf
Original Paper

Abstract

Assuming m − 1 < kp < m, we prove that the space C (M, N) of smooth mappings between compact Riemannian manifolds M, N (m = dim M) is dense in the Sobolev space W k,p(M, N) if and only if π m−1(N) = {0}. If π m−1(N) ≠ {0}, then every mapping in W k,p(M, N) can still be approximated by mappings MN which are smooth except in finitely many points.

Keywords

Sobolev space Manifolds Density 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department Mathematik der Friedrich-Alexander-UniversitätErlangenGermany

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