# Local minimizers of functionals with multiple volume constraints

Oudet, Édouard; Rieger, Marc Oliver (2008). Local minimizers of functionals with multiple volume constraints. ESAIM: Control, Optimisation and Calculus of Variations, 14(4):780-794.

## 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.

## 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.

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## Additional indexing

Item Type: Journal Article, refereed, original work 03 Faculty of Economics > Department of Banking and Finance 330 Economics Volume constrained problems, numerical simulations, level set method, local minima English 7 February 2008 05 Dec 2008 09:52 20 Jun 2016 17:46 EDP Sciences 1262-3377 https://doi.org/10.1051/cocv:2008013 http://www.esaim-cocv.org

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