A characterization of maps in \(H^ 1(B^ 3,S^ 2)\) which can be approximated by smooth maps
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Publication:920448
DOI10.1016/S0294-1449(16)30292-XzbMath0708.58004MaRDI QIDQ920448
Publication date: 1990
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=AIHPC_1990__7_4_269_0
Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Differentiable maps on manifolds (58C25)
Related Items (41)
RELAXING THE DIRICHLET ENERGY FOR MAPS INTO S2 IN HIGH DIMENSIONS ⋮ Density problems for W1,1 (M, N) ⋮ Existence of energy minimizers as stable knotted solitons in the Faddeev model ⋮ The interplay between analysis and topology in some nonlinear PDE problems ⋮ Sobolev bundles with Abelian structure groups ⋮ Energy with weight for \(S^2\)-valued maps with prescribed singularities ⋮ Everywhere discontinuous harmonic maps into spheres ⋮ The homological singularities of maps in trace spaces between manifolds ⋮ Sequential weak approximation for maps of finite Hessian energy ⋮ Relaxed energies for functionals on W1,1(B2, S1) ⋮ Some of my favorite open problems ⋮ A brief history of the Jacobian ⋮ Singularities of harmonic maps ⋮ Distances between classes in \(W^{1,1}(\Omega ;{\mathbb {S}}^{1})\) ⋮ Weak approximation by bounded Sobolev maps with values into complete manifolds ⋮ Some new properties of Sobolev mappings: intersection theoretical approach ⋮ \(\mathbb S^1\)-valued Sobolev maps ⋮ Uniform boundedness principles for Sobolev maps into manifolds ⋮ On the total variation of the Jacobian. ⋮ Weak closure of singular Abelian \(L ^{p }\)-bundles in 3 dimensions ⋮ A case of density in \(W^{2,p}(M;N)\) ⋮ Unnamed Item ⋮ Estimates for the topological degree and related topics ⋮ Topological singular set of vector-valued maps. I: Applications to manifold-constrained Sobolev and BV spaces ⋮ Improved partial regularity for manifold-constrained minimisers of subquadratic energies ⋮ Obstruction theory for the approximation and the deformation problems for Sobolev mappings ⋮ On the minimizers of the relaxed energy functional of mappings from higher dimensional balls into \(S^{2}\) ⋮ The relaxed energy for \(S^2\)-valued maps and measurable weights ⋮ Topological singular set of vector-valued maps. II: \( \varGamma \)-convergence for Ginzburg-Landau type functionals ⋮ A counterexample to the weak density of smooth maps between manifolds in Sobolev spaces ⋮ Density in \(W^{s, p}(\operatorname{\Omega}; N)\) ⋮ Density of Lipschitz mappings in the class of Sobolev mappings between metric spaces ⋮ Trace theory for Sobolev mappings into a manifold ⋮ Topological singularities for vector-valued Sobolev maps and applications ⋮ A problem of minimization with relaxed energy ⋮ Mapping problems, fundamental groups and defect measures ⋮ Weak notions of Jacobian determinant and relaxation ⋮ Energy estimate, energy gap phenomenon, and relaxed energy for Yang-Mills functional ⋮ On topological singular set of maps with finite 3-energy into \(S^3\) ⋮ Limiting behavior of the Ginzburg-Landau functional ⋮ Density of smooth maps for fractional Sobolev spaces \(W^{s, p}\) into \(\ell\) simply connected manifolds when \(s \geq 1\)
Cites Work
- A regularity theory for harmonic maps
- Infima of energy functionals in homotopy classes of mappings
- Harmonic maps with defects
- Density of smooth functions between two manifolds in Sobolev spaces
- Approximations of Sobolev maps between an open set and an Euclidean sphere, boundary data, and singularities
- The approximation problem for Sobolev maps between two manifolds
- Minimizing p-harmonic maps into spheres.
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