Given two compact Riemannian manifolds M-m, N-n without boundary and m - 1 <= 2p < m, we show that maps which are smooth except on finitely many points are dense in W-2,W-p(M;N). If, in addition, pi(m-1)(N) is trivial, then C-infinity(M;N) is dense in W-2,W-p(M;N).
Bousquet, P., Ponce, A., & Van Schaftingen, J. (2008). A case of density in W^{2,p}(M; N). Comptes rendus - Mathématique, 346(13-14), 735-740. https://doi.org/10.1016/j.crma.2008.05.006 (Original work published 2008)