Variational approximation of a functional of Mumford–Shah type in codimension higher than one

Francesco Ghiraldin

ESAIM: Control, Optimisation and Calculus of Variations (2014)

  • Volume: 20, Issue: 1, page 190-221
  • ISSN: 1292-8119

Abstract

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In this paper we consider a new kind of Mumford–Shah functional E(u, Ω) for maps u : ℝm → ℝn with m ≥ n. The most important novelty is that the energy features a singular set Su of codimension greater than one, defined through the theory of distributional jacobians. After recalling the basic definitions and some well established results, we prove an approximation property for the energy E(u, Ω) via Γ −convergence, in the same spirit of the work by Ambrosio and Tortorelli [L. Ambrosio and V.M. Tortorelli, Commun. Pure Appl. Math. 43 (1990) 999–1036].

How to cite

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Ghiraldin, Francesco. "Variational approximation of a functional of Mumford–Shah type in codimension higher than one." ESAIM: Control, Optimisation and Calculus of Variations 20.1 (2014): 190-221. <http://eudml.org/doc/272865>.

@article{Ghiraldin2014,
abstract = {In this paper we consider a new kind of Mumford–Shah functional E(u, Ω) for maps u : ℝm → ℝn with m ≥ n. The most important novelty is that the energy features a singular set Su of codimension greater than one, defined through the theory of distributional jacobians. After recalling the basic definitions and some well established results, we prove an approximation property for the energy E(u, Ω) via Γ −convergence, in the same spirit of the work by Ambrosio and Tortorelli [L. Ambrosio and V.M. Tortorelli, Commun. Pure Appl. Math. 43 (1990) 999–1036].},
author = {Ghiraldin, Francesco},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {jacobian; Γ-convergence; higher codimension; Mumford–Shah; Ginzburg–Landau; phase transition; Mumford-Shah-type functional; Jacobian; -convergence},
language = {eng},
number = {1},
pages = {190-221},
publisher = {EDP-Sciences},
title = {Variational approximation of a functional of Mumford–Shah type in codimension higher than one},
url = {http://eudml.org/doc/272865},
volume = {20},
year = {2014},
}

TY - JOUR
AU - Ghiraldin, Francesco
TI - Variational approximation of a functional of Mumford–Shah type in codimension higher than one
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2014
PB - EDP-Sciences
VL - 20
IS - 1
SP - 190
EP - 221
AB - In this paper we consider a new kind of Mumford–Shah functional E(u, Ω) for maps u : ℝm → ℝn with m ≥ n. The most important novelty is that the energy features a singular set Su of codimension greater than one, defined through the theory of distributional jacobians. After recalling the basic definitions and some well established results, we prove an approximation property for the energy E(u, Ω) via Γ −convergence, in the same spirit of the work by Ambrosio and Tortorelli [L. Ambrosio and V.M. Tortorelli, Commun. Pure Appl. Math. 43 (1990) 999–1036].
LA - eng
KW - jacobian; Γ-convergence; higher codimension; Mumford–Shah; Ginzburg–Landau; phase transition; Mumford-Shah-type functional; Jacobian; -convergence
UR - http://eudml.org/doc/272865
ER -

References

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