Lifting for manifold-valued maps of bounded variation

Canevari, Giacomo; Orlandi, Giandomenico

doi:10.1016/j.jfa.2019.108453

Cited by 4 publications

(1 citation statement)

References 31 publications

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“…The first main issue is to regularize the map u. Maps in BV .s S 1 / cannot always be approximated in energy by S 1 -valued smooth functions (in general they cannot be lifted without increasing the BV -norm [24,41]). Nonetheless, the result in [17] (see also [7]) guarantees the density of S 1 -valued maps that are smooth outside finitely many point-singularities.…”

Section: Introductionmentioning

confidence: 99%

Emergence of Concentration Effects in the Variational Analysis of theN‐Clock Model

Cicalese

Orlando

Ruf

2021

Comm Pure Appl Math

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We investigate the relationship between the N -clock model (also known as planar Potts model or Z N -model) and the XY model (at zero temperature) through a -convergence analysis of a suitable rescaling of the energy as both the number of particles and N diverge. We prove the existence of rates of divergence of N for which the continuum limits of the two models differ. With the aid of Cartesian currents we show that the asymptotics of the N -clock model in this regime features an energy that may concentrate on geometric objects of various dimensions. This energy prevails over the usual vortex-vortex interaction energy.

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Section: Introductionmentioning

confidence: 99%

Emergence of Concentration Effects in the Variational Analysis of theN‐Clock Model

Cicalese

Orlando

Ruf

2021

Comm Pure Appl Math

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Improved Partial Regularity for Manifold-Constrained Minimisers of Subquadratic Energies

Canevari

Orlandi

2020

Commun. Math. Phys.

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We consider minimising p-harmonic maps from three-dimensional domains to the real projective plane, for 1 < p < 2. These maps arise as least-energy configurations in variational models for nematic liquid crystals. We show that the singular set of such a map decomposes into a 1-dimensional set, which can be physically interpreted as a non-orientable line defect, and a locally finite set, i.e. a collection of point defects.

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Manifold-constrained free discontinuity problems and Sobolev approximation

Dipasquale,

Stroffolini

2024

Nonlinear Analysis

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Lifting for manifold-valued maps of bounded variation

Cited by 4 publications

References 31 publications

Emergence of Concentration Effects in the Variational Analysis of theN‐Clock Model

Emergence of Concentration Effects in the Variational Analysis of theN‐Clock Model

Improved Partial Regularity for Manifold-Constrained Minimisers of Subquadratic Energies

Manifold-constrained free discontinuity problems and Sobolev approximation

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