Rivière, Tristan Dense subsets of \(H^{1/2}(S^2,S^1)\). (English) Zbl 0960.35022 Ann. Global Anal. Geom. 18, No. 5, 517-528 (2000). Summary: We prove that the maps from \(S^2\) into \(S^1\) having a finite number of isolated singularities of degree \(\pm 1\) are dense for the strong topology in \(H^{1/2}(S^2, S^1)\). We also prove that smooth maps are dense in \(H^{1/2}(S^2, S^1)\) for the sequentially weak topology and that this is not the case in \(H^s(S^2, S^1)\) for \(s> 1/2\). Cited in 1 ReviewCited in 26 Documents MSC: 35J20 Variational methods for second-order elliptic equations 35J67 Boundary values of solutions to elliptic equations and elliptic systems 35J60 Nonlinear elliptic equations 58-XX Global analysis, analysis on manifolds 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 46E40 Spaces of vector- and operator-valued functions Keywords:density problems; Ginzburg-Landau functional; minimal connections; Sobolev maps between manifolds; Sobolev spaces; topological singularities; trace spaces PDF BibTeX XML Cite \textit{T. Rivière}, Ann. Global Anal. Geom. 18, No. 5, 517--528 (2000; Zbl 0960.35022) Full Text: DOI OpenURL