# Strong density for higher order Sobolev spaces into compact manifolds

Pierre Bousquet; Augusto C. Ponce; Jean Van Schaftingen

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 4, page 763-817
- ISSN: 1435-9855

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topBousquet, 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 -

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