Geodesic
Strong density for higher order Sobolev spaces into compact manifolds
Journal of the European Mathematical Society, Tome 17 (2015) no. 4, pp. 763-817

Voir la notice de l'article provenant de la source EMS Press

Given a compact manifold Nn, an integer k∈N∗​ and an exponent 1≤p∞, we prove that the class C∞(Q​m;Nn) of smooth maps on the cube with values into Nn is dense with respect to the strong topology in the Sobolev space Wk,p(Qm;Nn) when the homotopy group π⌊kp⌋​(Nn) of order ⌊kp⌋ is trivial. We also prove density of maps that are smooth except for a set of dimension m−⌊kp⌋−1, without any restriction on the homotopy group of Nn.
DOI : 10.4171/jems/518
Classification : 58-XX, 46-XX
Keywords: Strong density, Sobolev maps, higher order Sobolev spaces, homotopy, topological singularity 
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     author = {Pierre Bousquet and Augusto C. Ponce and Jean Van Schaftingen},
     title = {Strong density for higher order {Sobolev} spaces into compact manifolds},
     journal = {Journal of the European Mathematical Society},
     pages = {763--817},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2015},
     doi = {10.4171/jems/518},
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Pierre Bousquet; Augusto C. Ponce; Jean Van Schaftingen. Strong density for higher order Sobolev spaces into compact manifolds. Journal of the European Mathematical Society, Tome 17 (2015) no. 4, pp. 763-817. doi: 10.4171/jems/518

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