Given a compact manifold and real numbers and , we prove that the class of smooth maps on the cube with values into is strongly dense in the fractional Sobolev space when is simply connected. For integer, we prove weak sequential density of when is simply connected. The proofs are based on the existence of a retraction of onto except for a small subset of and on a pointwise estimate of fractional derivatives of composition of maps in .
Revised:
Accepted:
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Keywords: Strong density; weak sequential density; Sobolev maps; fractional Sobolev spaces; simply connectedness
Pierre Bousquet 1; Augusto C. Ponce 2; Jean Van Schaftingen 2
@article{CML_2013__5_2_3_0, author = {Pierre Bousquet and Augusto C. Ponce and Jean Van Schaftingen}, title = {Density of smooth maps for fractional {Sobolev} spaces $W^{s, p}$ into $\ell $ simply connected manifolds when $s \ge 1$}, journal = {Confluentes Mathematici}, pages = {3--24}, publisher = {Institut Camille Jordan}, volume = {5}, number = {2}, year = {2013}, doi = {10.5802/cml.5}, language = {en}, url = {https://cml.centre-mersenne.org/articles/10.5802/cml.5/} }
TY - JOUR AU - Pierre Bousquet AU - Augusto C. Ponce AU - Jean Van Schaftingen TI - Density of smooth maps for fractional Sobolev spaces $W^{s, p}$ into $\ell $ simply connected manifolds when $s \ge 1$ JO - Confluentes Mathematici PY - 2013 SP - 3 EP - 24 VL - 5 IS - 2 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.5/ DO - 10.5802/cml.5 LA - en ID - CML_2013__5_2_3_0 ER -
%0 Journal Article %A Pierre Bousquet %A Augusto C. Ponce %A Jean Van Schaftingen %T Density of smooth maps for fractional Sobolev spaces $W^{s, p}$ into $\ell $ simply connected manifolds when $s \ge 1$ %J Confluentes Mathematici %D 2013 %P 3-24 %V 5 %N 2 %I Institut Camille Jordan %U https://cml.centre-mersenne.org/articles/10.5802/cml.5/ %R 10.5802/cml.5 %G en %F CML_2013__5_2_3_0
Pierre Bousquet; Augusto C. Ponce; Jean Van Schaftingen. Density of smooth maps for fractional Sobolev spaces $W^{s, p}$ into $\ell $ simply connected manifolds when $s \ge 1$. Confluentes Mathematici, Volume 5 (2013) no. 2, pp. 3-24. doi : 10.5802/cml.5. https://cml.centre-mersenne.org/articles/10.5802/cml.5/
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