Topological singular set of vector-valued maps, I: applications to manifold-constrained Sobolev and BV spaces View Full Text


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Article Info

DATE

2019-04

AUTHORS

Giacomo Canevari, Giandomenico Orlandi

ABSTRACT

We introduce an operator S on vector-valued maps u which has the ability to capture the relevant topological information carried by u. In particular, this operator is defined on maps that take values in a closed submanifold N of the Euclidean space Rm, and coincides with the distributional Jacobian in case N is a sphere. More precisely, the range of S is a set of maps whose values are flat chains with coefficients in a suitable normed abelian group. In this paper, we use S to characterise strong limits of smooth, N-valued maps with respect to Sobolev norms, extending a result by Pakzad and Rivière. We also discuss applications to the study of manifold-valued maps of bounded variation. In a companion paper, we will consider applications to the asymptotic behaviour of minimisers of Ginzburg–Landau type functionals, with N-well potentials. More... »

PAGES

72

References to SciGraph publications

  • 2002-03. The Jacobian and the Ginzburg-Landau energy in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 1999-09. Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents in JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
  • 2010-04. Landau–De Gennes Theory of Nematic Liquid Crystals: the Oseen–Frank Limit and Beyond in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1995-09. Degree theory and BMO; part I: Compact manifolds without boundaries in SELECTA MATHEMATICA
  • 2003-03. Topology of sobolev mappings, II in ACTA MATHEMATICA
  • 2019-04. Lifting of RPd-1-valued maps in BV and applications to uniaxial Q-tensors. With an appendix on an intrinsic BV-energy for manifold-valued maps in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 2000-10. Dense Subsets of H1/2(S2, S1) in ANNALS OF GLOBAL ANALYSIS AND GEOMETRY
  • 1999-09. The deformation theorem for flat chains in ACTA MATHEMATICA
  • 1991-12. The approximation problem for Sobolev maps between two manifolds in ACTA MATHEMATICA
  • 2000-12. Lifting in Sobolev spaces in JOURNAL D'ANALYSE MATHÉMATIQUE
  • 2003-02. Weak density of smooth maps for the Dirichlet energy between manifolds in GEOMETRIC AND FUNCTIONAL ANALYSIS
  • 2008-01. Flat Chains in Banach Spaces in THE JOURNAL OF GEOMETRIC ANALYSIS
  • 1986-12. Existence and partial regularity of static liquid crystal configurations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2003-03. Weak Density of Smooth Maps in W1, 1(M,N) for Non-Abelian π1(N) in ANNALS OF GLOBAL ANALYSIS AND GEOMETRY
  • 2017-02. Line Defects in the Small Elastic Constant Limit of a Three-Dimensional Landau-de Gennes Model in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2014-03. A new obstruction to the extension problem for Sobolev maps between manifolds in JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
  • 2014-08. On Minimizers of a Landau–de Gennes Energy Functional on Planar Domains in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2011-11. Orientability and Energy Minimization in Liquid Crystal Models in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2011-07. The Jacobian determinant revisited in INVENTIONES MATHEMATICAE
  • 2003-09. Functions with prescribed singularities in JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
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    http://scigraph.springernature.com/pub.10.1007/s00526-019-1501-8

    DOI

    http://dx.doi.org/10.1007/s00526-019-1501-8

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    https://app.dimensions.ai/details/publication/pub.1112918638


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