Density of smooth functions between two manifolds in Sobolev spaces
From MaRDI portal
Publication:1110775
DOI10.1016/0022-1236(88)90065-1zbMath0657.46027OpenAlexW2032886359MaRDI QIDQ1110775
Xiaomin Zheng, Fabrice Bethuel
Publication date: 1988
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0022-1236(88)90065-1
Related Items (only showing first 100 items - show all)
ON NEMATICS STABILIZED BY A LARGE EXTERNAL FIELD ⋮ On global singularities of Sobolev mappings ⋮ Minimizing the energy of maps from a surface into a 2-sphere with prescribed degree and boundary values ⋮ Density problems for W1,1 (M, N) ⋮ \(H^{1/2}\) maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation ⋮ Distances between classes of sphere-valued Sobolev maps ⋮ Homogenization of variational problems in manifold valued \(BV\)-spaces ⋮ The square root normal field distance and unbalanced optimal transport ⋮ Equivalent statement of the Poincaré conjecture ⋮ Unnamed Item ⋮ The interplay between analysis and topology in some nonlinear PDE problems ⋮ Compactness, Kinetic Formulation, and Entropies for a Problem Related to Micromagnetics ⋮ Singularities for \(p\)-energy minimizing unit vector fields on planar domains ⋮ Sobolev bundles with Abelian structure groups ⋮ Degree theory of BMO. I: Compact manifolds without boundaries ⋮ Extensions for Sobolev mappings between manifolds ⋮ Smooth approximation of Orlicz-Sobolev maps between manifolds ⋮ A note on weak approximation of minors ⋮ On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target ⋮ Approximations of Sobolev maps between an open set and an Euclidean sphere, boundary data, and singularities ⋮ Approximation in area of graphs with isolated singularities ⋮ Bloch bundles, Marzari-Vanderbilt functional and maximally localized Wannier functions ⋮ Everywhere discontinuous harmonic maps into spheres ⋮ Renormalized energy between vortices in some Ginzburg-Landau models on 2-dimensional Riemannian manifolds ⋮ The Dirichlet energy of mappings with values into the sphere ⋮ Approximation of sobolev mappings ⋮ A chromaticity-brightness model for color images denoising in a Meyer's ``\(u + v\) framework ⋮ Homotopy classification of minimizers of the Ginzburg-Landau energy and the existence of permanent currents ⋮ Limiting domain wall energy for a problem related to micromagnetics ⋮ Junction of ferromagnetic thin films ⋮ Edge domain walls in ultrathin exchange-biased films ⋮ Density of bounded maps in Sobolev spaces into complete manifolds ⋮ Topological and analytical properties of Sobolev bundles. II. Higher dimensional cases ⋮ Sequential weak approximation for maps of finite Hessian energy ⋮ Asymptotic analysis for two joined thin slanting ferromagnetic films ⋮ Relaxed energies for functionals on W1,1(B2, S1) ⋮ Density of smooth maps in \(W^{k,p}(M, N)\) for a close to critical domain dimension ⋮ Two-dimensional unit-length vector fields of vanishing divergence ⋮ Approximations in trace spaces defined between manifolds ⋮ Minimal BV-liftings of \(W^{1, 1} (\Omega, \mathbb{S}^1)\) maps in 2D are ``often unique ⋮ Distances between classes in \(W^{1,1}(\Omega ;{\mathbb {S}}^{1})\) ⋮ Relaxation in SBV\(_{p } (\varOmega ; S ^{d-1})\) ⋮ Some new properties of Sobolev mappings: intersection theoretical approach ⋮ Gradient vector fields with values into \(S^1\) ⋮ A zigzag pattern in micromagnetics ⋮ Unnamed Item ⋮ Area-minimizing disks with free boundary and prescribed enclosed volume ⋮ A characterization of maps in \(H^ 1(B^ 3,S^ 2)\) which can be approximated by smooth maps ⋮ \(\mathbb S^1\)-valued Sobolev maps ⋮ Lifting of BV functions with values in \(S^1\) ⋮ Torus-like solutions for the Landau-de Gennes model. I: The Lyuksyutov regime ⋮ On a new harmonic heat flow with the reverse Hölder inequalities ⋮ Homotopy groups of spheres and Lipschitz homotopy groups of Heisenberg groups ⋮ A kinetic energy reduction technique and characterizations of the ground states of spin-1 Bose-Einstein condensates ⋮ Regularity of minimizers of relaxed problems for harmonic maps ⋮ Global Jacobian and \(\Gamma\)-convergence in a two-dimensional Ginzburg-Landau model for boundary vortices ⋮ Magnetic domains in thin ferromagnetic films with strong perpendicular anisotropy ⋮ A case of density in \(W^{2,p}(M;N)\) ⋮ Convergence of an implicit, constraint preserving finite element discretization of \(p\)-harmonic heat flow into spheres ⋮ The approximation problem for Sobolev maps between two manifolds ⋮ Strong approximation of fractional Sobolev maps ⋮ Estimates for the topological degree and related topics ⋮ Improved partial regularity for manifold-constrained minimisers of subquadratic energies ⋮ Lifting in Besov spaces ⋮ Line defects in the small elastic constant limit of a three-dimensional Landau-de Gennes model ⋮ Topological singularities in \(W^{S,P}(S^N,S^{1})\) ⋮ Sobolev mappings, degree, homotopy classes and rational homology spheres ⋮ The distance between homotopy classes of \(S^{1}\)-valued maps in multiply connected domains ⋮ Regularity and relaxed problems of minimizing biharmonic maps into spheres ⋮ The relaxed energy for \(S^2\)-valued maps and measurable weights ⋮ Local minimizers and quasiconvexity -- the impact of topology ⋮ Analysis of nematic liquid crystals with disclination lines ⋮ Decomposition of \(\mathbb S^1\)-valued maps in Sobolev spaces ⋮ Néel and Cross-Tie Wall Energies for Planar Micromagnetic Configurations ⋮ Homogenization of variational problems in manifold valued Sobolev spaces ⋮ Sobolev Mappings between Manifolds and Metric Spaces ⋮ Asymptotic analysis, in a thin multidomain, of minimizing maps with values in \(S^2\) ⋮ The strong \(L^p\)-closure of vector fields with finitely many integer singularities on \(B^3\) ⋮ Weighted spectral gap for magnetic Schrödinger operators with a potential term ⋮ 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 ⋮ Topological singularities for vector-valued Sobolev maps and applications ⋮ Prescribing the Jacobian in critical spaces ⋮ Lifting for manifold-valued maps of bounded variation ⋮ A problem of minimization with relaxed energy ⋮ Hölder-topology of the Heisenberg group ⋮ Higher order intrinsic weak differentiability and Sobolev spaces between manifolds ⋮ Energy minimisers with prescribed Jacobian ⋮ Unnamed Item ⋮ Topological singularities in periodic media: Ginzburg-Landau and core-radius approaches ⋮ Convergence of a class of degenerate Ginzburg-Landau functionals and regularity for a subelliptic harmonic map equation ⋮ Ginzburg-Landau vortices: Weak stability and Schrödinger equation dynamics ⋮ Lifting in Sobolev spaces ⋮ On topological singular set of maps with finite 3-energy into \(S^3\) ⋮ Density of smooth maps for fractional Sobolev spaces \(W^{s, p}\) into \(\ell\) simply connected manifolds when \(s \geq 1\) ⋮ \(W^{1,p}\) convergence of Ginzburg--Landau type minimizers ⋮ Strong density for higher order Sobolev spaces into compact manifolds ⋮ Topologically driven local minimizers of the Oseen-Frank energy ⋮ Homomorphism between homotopy groups induced by elements of the Sobolev space \(L^{1,p}(M,N)\)
Cites Work
This page was built for publication: Density of smooth functions between two manifolds in Sobolev spaces
