Given a compact manifold , an integer and an exponent , we prove that the class of smooth maps on the cube with values into is dense with respect to the strong topology in the Sobolev space when the homotopy group of order is trivial. We also prove density of maps that are smooth except for a set of dimension , without any restriction on the homotopy group of .
Cite this article
Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen, Strong density for higher order Sobolev spaces into compact manifolds. J. Eur. Math. Soc. 17 (2015), no. 4, pp. 763–817DOI 10.4171/JEMS/518