Given two compact Riemannian manifolds without boundary and , we show that maps which are smooth except on finitely many points are dense in . If, in addition, is trivial, then is dense in .
On considère deux variétés riemaniennes compactes sans bord et . Quand , on montre que les fonctions lisses sauf en un nombre fini de points sont denses dans . Si la variété N vérifie , alors est dense dans .
Published online:
Pierre Bousquet 1; Augusto C. Ponce 2; Jean Van Schaftingen 3
@article{CRMATH_2008__346_13-14_735_0, author = {Pierre Bousquet and Augusto C. Ponce and Jean Van Schaftingen}, title = {A case of density in $ {W}^{2,p}(M;N)$}, journal = {Comptes Rendus. Math\'ematique}, pages = {735--740}, publisher = {Elsevier}, volume = {346}, number = {13-14}, year = {2008}, doi = {10.1016/j.crma.2008.05.006}, language = {en}, }
Pierre Bousquet; Augusto C. Ponce; Jean Van Schaftingen. A case of density in $ {W}^{2,p}(M;N)$. Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 735-740. doi : 10.1016/j.crma.2008.05.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.05.006/
[1] A characterization of maps in which can be approximated by smooth maps, Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 7 (1990), pp. 269-286
[2] The approximation problem for Sobolev maps between two manifolds, Acta Math., Volume 167 (1991), pp. 153-206
[3] A cohomological criterion for density of smooth maps in Sobolev spaces between two manifolds, Orsay, 1990 (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.), Volume vol. 332 (1990), pp. 15-23
[4] Density of smooth functions between two manifolds in Sobolev spaces, J. Funct. Anal., Volume 80 (1988), pp. 60-75
[5] P. Bousquet, A.C. Ponce, J. Van Schaftingen, Strong density in , in preparation
[6] Harmonic maps with defects, Commun. Math. Phys., Volume 107 (1986), pp. 649-705
[7] Degree theory and BMO. I. Compact manifolds without boundaries. Selecta Math. (N.S.), 1 (1995), pp. 197-263
[8] Topology of Sobolev mappings. II, Acta Math., Volume 191 (2003), pp. 55-107
[9] Sobolev maps on manifolds: degree, approximation, lifting, Perspectives in Nonlinear Partial Differential Equations, Contemp. Math., vol. 446, Amer. Math. Soc., Providence, RI, 2007, pp. 413-436 (In honor of Haïm Brezis)
[10] Boundary regularity and the Dirichlet problem for harmonic maps, J. Differential Geom., Volume 18 (1983), pp. 253-268
Cited by Sources:
Comments - Policy