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Issue ESAIM: COCV
Volume 14, Number 4, October-December 2008
Page(s) 780 - 794
DOI 10.1051/cocv:2008013
Published online 07 February 2008

ESAIM: COCV 14 (2008) 780-794
DOI: 10.1051/cocv:2008013

Local minimizers of functionals with multiple volume constraints

Édouard Oudet1 and Marc Oliver Rieger2

1  Université de Savoie, France; Edouard.Oudet@univ-savoie.fr
2  University of Zürich, ISB, Switzerland; rieger@isb.uzh.ch


Received November 19, 2006. Revised June 14, 2007. Published online February 7, 2008.

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 $\Gamma$-limit argument and illustrate this with numerical computations. Finally we construct explicitly local and global minimizers for problems with two volume constraints.


Mathematics Subject Classification. 49J, 65K10

Key words: Volume constrained problems, numerical simulations, level set method, local minima


© EDP Sciences, SMAI 2008


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