Strong density for higher order Sobolev spaces into compact manifolds

Bousquet, Pierre, Ponce, Augusto C., and Van Schaftingen, Jean. "Strong density for higher order Sobolev spaces into compact manifolds." Journal of the European Mathematical Society 017.4 (2015): 763-817. <http://eudml.org/doc/277624>.

@article{Bousquet2015,
abstract = {Given a compact manifold $N^n$, an integer $k \in \mathbb \{N\}_*$ and an exponent $1 \le p < \infty $, we prove that the class $C^\infty (\overline\{Q\}^m; N^n)$ of smooth maps on the cube with values into $N^n$ is dense with respect to the strong topology in the Sobolev space $W^\{k, p\}(Q^m; N^n)$ when the homotopy group $\pi _\{\lfloor kp \rfloor \}(N^n)$ of order $\lfloor kp \rfloor $ is trivial. We also prove density of maps that are smooth except for a set of dimension $m - \lfloor kp \rfloor - 1$, without any restriction on the homotopy group of $N^n$.},
author = {Bousquet, Pierre, Ponce, Augusto C., Van Schaftingen, Jean},
journal = {Journal of the European Mathematical Society},
keywords = {strong density; Sobolev maps; higher order Sobolev spaces; homotopy; topological singularity; strong density; Sobolev maps; higher order Sobolev spaces; Sobolev metric; homotopy; topological singularity},
language = {eng},
number = {4},
pages = {763-817},
publisher = {European Mathematical Society Publishing House},
title = {Strong density for higher order Sobolev spaces into compact manifolds},
url = {http://eudml.org/doc/277624},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Bousquet, Pierre
AU - Ponce, Augusto C.
AU - Van Schaftingen, Jean
TI - Strong density for higher order Sobolev spaces into compact manifolds
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 4
SP - 763
EP - 817
AB - Given a compact manifold $N^n$, an integer $k \in \mathbb {N}_*$ and an exponent $1 \le p < \infty $, we prove that the class $C^\infty (\overline{Q}^m; N^n)$ of smooth maps on the cube with values into $N^n$ is dense with respect to the strong topology in the Sobolev space $W^{k, p}(Q^m; N^n)$ when the homotopy group $\pi _{\lfloor kp \rfloor }(N^n)$ of order $\lfloor kp \rfloor $ is trivial. We also prove density of maps that are smooth except for a set of dimension $m - \lfloor kp \rfloor - 1$, without any restriction on the homotopy group of $N^n$.
LA - eng
KW - strong density; Sobolev maps; higher order Sobolev spaces; homotopy; topological singularity; strong density; Sobolev maps; higher order Sobolev spaces; Sobolev metric; homotopy; topological singularity
UR - http://eudml.org/doc/277624
ER -