Strong approximation of fractional Sobolev maps

DOI10.1007/s11784-014-0172-5zbMath1310.58006arXiv1310.6017OpenAlexW3098139229MaRDI QIDQ490044

Augusto C. Ponce, Pierre Bousquet, Jean Van Schaftingen

Publication date: 21 January 2015

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.6017

zbMATH Keywords

fractional Sobolev spacesSobolev mapssimply connectednessstrong density

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) Manifolds of mappings (58D15)

Related Items

Well-posedness of a fractional porous medium equation on an evolving surface ⋮ Partial regularity for holonomic minimisers of quasiconvex functionals ⋮ Fractional Orlicz-Sobolev embeddings ⋮ On fractional Orlicz‑Sobolev spaces ⋮ Boundedness of functions in fractional Orlicz-Sobolev spaces ⋮ On fractional Orlicz-Sobolev spaces ⋮ Density in \(W^{s, p}(\operatorname{\Omega}; N)\) ⋮ Trace theory for Sobolev mappings into a manifold ⋮ On the multiple existence of superquadratic Dirac-harmonic maps into flat tori ⋮ Quantitative characterization of traces of Sobolev maps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in \(n\) variabili
• Boundary regularity and the Dirichlet problem for harmonic maps
• Strong density results in trace spaces of maps between manifolds
• Density of smooth functions between two manifolds in Sobolev spaces
• Every superposition operator mapping one Sobolev space into another is continuous
• The approximation problem for Sobolev maps between two manifolds
• On the Brezis and Mironescu conjecture concerning a Gagliardo--Nirenberg inequality for fractional Sobolev norms.
• Lifting in Sobolev spaces
• Dense subsets of \(H^{1/2}(S^2,S^1)\)
• Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces
• An elementary proof of the Brezis and Mironescu theorem on the composition operator in fractional Sobolev spaces
• \(H^{1/2}\) maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation
• Topology of Sobolev mappings. II.
• Degree theory of BMO. I: Compact manifolds without boundaries
• Wavelets and Besov spaces
• Density of smooth maps for fractional Sobolev spaces \(W^{s, p}\) into \(\ell\) simply connected manifolds when \(s \geq 1\)
• Strong density for higher order Sobolev spaces into compact manifolds
• Density results for the \(W^{1/2}\) energy of maps into a manifold
• Mappings minimizing theLp norm of the gradient
• Approximation of sobolev mappings
• Approximations in trace spaces defined between manifolds

This page was built for publication: Strong approximation of fractional Sobolev maps