Local minimizers of functionals with multiple volume constraints

Édouard Oudet; Marc Oliver Rieger

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 14, Issue: 4, page 780-794
  • ISSN: 1292-8119

Abstract

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We study variational problems with volume constraints, i.e., with level sets of prescribed measure. We introduce a numerical method to approximate local minimizers and illustrate it with some two-dimensional examples. We demonstrate numerically nonexistence results which had been obtained analytically in previous work. Moreover, we show the existence of discontinuous dependence of global minimizers from the data by using a Γ-limit argument and illustrate this with numerical computations. Finally we construct explicitly local and global minimizers for problems with two volume constraints.

How to cite

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Oudet, Édouard, and Rieger, Marc Oliver. "Local minimizers of functionals with multiple volume constraints." ESAIM: Control, Optimisation and Calculus of Variations 14.4 (2008): 780-794. <http://eudml.org/doc/250315>.

@article{Oudet2008,
abstract = { We study variational problems with volume constraints, i.e., with level sets of prescribed measure. We introduce a numerical method to approximate local minimizers and illustrate it with some two-dimensional examples. We demonstrate numerically nonexistence results which had been obtained analytically in previous work. Moreover, we show the existence of discontinuous dependence of global minimizers from the data by using a Γ-limit argument and illustrate this with numerical computations. Finally we construct explicitly local and global minimizers for problems with two volume constraints. },
author = {Oudet, Édouard, Rieger, Marc Oliver},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Volume constrained problems; numerical simulations; level set method; local minima; volume constrained problems},
language = {eng},
month = {2},
number = {4},
pages = {780-794},
publisher = {EDP Sciences},
title = {Local minimizers of functionals with multiple volume constraints},
url = {http://eudml.org/doc/250315},
volume = {14},
year = {2008},
}

TY - JOUR
AU - Oudet, Édouard
AU - Rieger, Marc Oliver
TI - Local minimizers of functionals with multiple volume constraints
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/2//
PB - EDP Sciences
VL - 14
IS - 4
SP - 780
EP - 794
AB - We study variational problems with volume constraints, i.e., with level sets of prescribed measure. We introduce a numerical method to approximate local minimizers and illustrate it with some two-dimensional examples. We demonstrate numerically nonexistence results which had been obtained analytically in previous work. Moreover, we show the existence of discontinuous dependence of global minimizers from the data by using a Γ-limit argument and illustrate this with numerical computations. Finally we construct explicitly local and global minimizers for problems with two volume constraints.
LA - eng
KW - Volume constrained problems; numerical simulations; level set method; local minima; volume constrained problems
UR - http://eudml.org/doc/250315
ER -

References

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