Topological singularities for vector-valued Sobolev maps and applications

DOI10.5802/afst.1677zbMath1471.58009OpenAlexW3179080108MaRDI QIDQ2046378

Giandomenico Orlandi, Giacomo Canevari

Publication date: 17 August 2021

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5802/afst.1677

zbMATH Keywords

variational problemlifting problemLandau-de Gennes modelflat chainstopological singularitiesSobolev mapmanifold-valued mapsGinzburg-Landau type functionals

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Set-valued and function-space-valued mappings on manifolds (58C06)

Cites Work

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• Partial regularity for holonomic minimisers of quasiconvex functionals
• Stability of point defects of degree \(\pm \frac{1}{2}\) in a two-dimensional nematic liquid crystal model
• Line defects in the small elastic constant limit of a three-dimensional Landau-de Gennes model
• The Jacobian determinant revisited
• Orientability and energy minimization in liquid crystal models
• On minimizers of a Landau-de Gennes energy functional on planar domains
• Maps into projective spaces: liquid crystal and conformal energies
• The imbedding problem for Riemannian manifolds
• Vortices in the magnetic Ginzburg-Landau model
• A characterization of maps in \(H^ 1(B^ 3,S^ 2)\) which can be approximated by smooth maps
• A note on closed isometric embeddings
• Landau-De Gennes theory of nematic liquid crystals: the Oseen-Frank limit and beyond
• Harmonic maps with defects
• Existence and partial regularity of static liquid crystal configurations
• Density of smooth functions between two manifolds in Sobolev spaces
• Level set approach to mean curvature flow in arbitrary codimension
• The approximation problem for Sobolev maps between two manifolds
• Convexity conditions and existence theorems in nonlinear elasticity
• Weak density of smooth maps for the Dirichlet energy between manifolds
• Functions with prescribed singularities
• Lifting of BV functions with values in \(S^1\)
• The deformation theorem for flat chains
• Dense subsets of \(H^{1/2}(S^2,S^1)\)
• The Jacobian and the Ginzburg-Landau energy
• Lifting of \({\mathbb {RP}^{d-1}}\)-valued maps in \(BV\) and applications to uniaxial \(Q\)-tensors. With an appendix on an intrinsic \(BV\)-energy for manifold-valued maps
• Topological singular set of vector-valued maps. I: Applications to manifold-constrained Sobolev and BV spaces
• Rectifiability of flat chains
• Extensions for Sobolev mappings between manifolds
• Refined approximation for minimizers of a Landau-de Gennes energy functional
• Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents
• Lifting in Besov spaces
• Topological singular set of vector-valued maps. II: \( \varGamma \)-convergence for Ginzburg-Landau type functionals
• Existence and limiting behavior of min-max solutions of the Ginzburg-Landau equations on compact manifolds
• Ginzburg-Landau functionals and renormalized energy: a revised \({\gamma}\)-convergence approach
• Stability of the melting hedgehog in the Landau-de Gennes theory of nematic liquid crystals
• Analysis of nematic liquid crystals with disclination lines
• Lifting for manifold-valued maps of bounded variation
• Density of smooth maps for fractional Sobolev spaces \(W^{s, p}\) into \(\ell\) simply connected manifolds when \(s \geq 1\)
• The space \(\operatorname{BV}(S^2,S^1)\): minimal connection and optimal lifting
• Convergence of the parabolic Ginzburg-Landau equation to motion by mean curvature
• Normal and integral currents
• Renormalized energy between vortices in some Ginzburg-Landau models on 2-dimensional Riemannian manifolds
• Minimal submanifolds from the abelian Higgs model
• A quantization property for static Ginzburg-Landau vortices
• Representing Three-Dimensional Cross Fields Using Fourth Order Tensors
• Mappings minimizing theLp norm of the gradient
• Functions of bounded higher variation
• On the structure of the Sobolev space H1/2 with values into the circle
• Lifting, degree, and distributional Jacobian revisited
• On the covergence of minimizers of singular perturbation functionals
• Biaxiality in the asymptotic analysis of a 2D Landau−de Gennes model for liquid crystals
• Flat Chains Over a Finite Coefficient Group
• The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension
• Variational convergence for functionals of Ginzburg-Landau type
• 𝑄 valued functions minimizing Dirichlet’s integral and the regularity of area minimizing rectifiable currents up to codimension two
• Ginzburg-Landau vortices
• Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions
• Function spaces for liquid crystals

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