Density of bounded maps in Sobolev spaces into complete manifolds

Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen

Given a complete noncompact Riemannian manifold $N^n$, we investigate whether the set of bounded Sobolev maps $(W^{1,p}\cap L^{\infty })(Q^m;N^n)$ on the cube $Q^m$ is strongly de…