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Density of smooth functions between two manifolds in Sobolev spaces. (English) Zbl 0657.46027

Author’s summary: We give some results concerning density or non-density of smooth functions between two compact manifolds \(M^ n\) and \(N^ k\) in Sobolev spaces \(W^{1,p}(M^ n,N^ k)\). In particular, we study the case \(N=S^ k\).
Reviewer: J.Włoka

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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[1] Eells, J; Lemaire, L, Bull. London math. soc., 10, 1-68, (1978)
[2] Schoen, R; Uhlenbeck, K, Boundary regularity and the Dirichlet problem for harmonic maps, J. differential geom., 18, 253-268, (1983) · Zbl 0547.58020
[3] {\scR. Schoen and K. Uhlenbeck}, Approximation theorems for Sobolev mappings, preprint. · Zbl 0521.58021
[4] Bethuel, F; Zheng, X, Sur la densité des fonctions régulières entre deux variétés dans des expaces de Sobolev, C.R. acad. sci. Paris, 303, 447-449, (1986) · Zbl 0595.46036
[5] Brezis, H; Coron, J-M; Lieb, E, Harmonic maps with defects, Comm. math. phys., 107, 649-705, (1986) · Zbl 0608.58016
[6] {\scM. Escobedo}, in preparation.
[7] {\scB. White}, Infima of energy functionals in homotopy classes, preprint. · Zbl 0588.58017
[8] {\scR. Hardt and F. H. Lin}, Mappings that minimize the pth power of the gradient, preprint.
[9] Hardt, R; Kinderlehrer, D; Lin, F.H, Existence and partial regularity of static liquid crystal configurations, Comm. math. phys., 105, 547-570, (1986) · Zbl 0611.35077
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