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Local minimizers of functionals with multiple volume constraints

Published online by Cambridge University Press:  07 February 2008

Édouard Oudet  and
Marc Oliver Rieger
Édouard Oudet
Affiliation:
Université de Savoie, France; Edouard.Oudet@univ-savoie.fr
Marc Oliver Rieger
Affiliation:
University of Zürich, ISB, Switzerland; rieger@isb.uzh.ch
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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.

Keywords

Volume constrained problemsnumerical simulationslevel set methodlocal minima
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 4 , October 2008 , pp. 780 - 794
Copyright
© EDP Sciences, SMAI, 2008

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