Strong density for higher order Sobolev spaces into compact manifolds

DOI10.4171/JEMS/518zbMath1318.58006arXiv1203.3721MaRDI QIDQ2344497

Augusto C. Ponce, Jean Van Schaftingen, Pierre Bousquet

Publication date: 15 May 2015

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.3721

zbMATH Keywords

homotopySobolev mapstopological singularitystrong densitySobolev metrichigher order Sobolev spaces

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Continuous and differentiable maps in nonlinear functional analysis (46T20) Differentiable maps on manifolds (58C25) Manifolds of mappings (58D15)

Related Items (15)

Partial regularity of polyharmonic maps to targets of sufficiently simple topology ⋮ Density of bounded maps in Sobolev spaces into complete manifolds ⋮ Sequential weak approximation for maps of finite Hessian energy ⋮ Asymptotic behavior of minimizing \(p\)-harmonic maps when \(p \nearrow 2\) in dimension 2 ⋮ Heat flow of extrinsic biharmonic maps from a four dimensional manifold with boundary ⋮ Minimal Ws,ns$W^{s,\frac{n}{s}}$‐harmonic maps in homotopy classes ⋮ Weak approximation by bounded Sobolev maps with values into complete manifolds ⋮ Uniform boundedness principles for Sobolev maps into manifolds ⋮ Strong approximation of fractional Sobolev maps ⋮ Density in \(W^{s, p}(\operatorname{\Omega}; N)\) ⋮ Prescribing the Jacobian in critical spaces ⋮ Hölder-topology of the Heisenberg group ⋮ Higher order intrinsic weak differentiability and Sobolev spaces between manifolds ⋮ Density of smooth maps for fractional Sobolev spaces \(W^{s, p}\) into \(\ell\) simply connected manifolds when \(s \geq 1\) ⋮ Quantitative characterization of traces of Sobolev maps

Cites Work

• Orientability and energy minimization in liquid crystal models
• A case of density in \(W^{2,p}(M;N)\)
• A regularity result for polyharmonic maps with higher integrability
• Density of smooth functions between two manifolds in Sobolev spaces
• The approximation problem for Sobolev maps between two manifolds
• Density of smooth maps for fractional Sobolev spaces \(W^{s, p}\) into \(\ell\) simply connected manifolds when \(s \geq 1\)
• Lifting, degree, and distributional Jacobian revisited

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