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| Type | Journal Article |
| Scope | Discipline-based scholarship |
| Title | Local minimizers of functionals with multiple volume constraints |
| Organization Unit | |
| Authors |
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| Item Subtype | Original Work |
| Refereed | Yes |
| Status | Published in final form |
| Language |
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| Journal Title | ESAIM: Control, Optimisation and Calculus of Variations |
| Publisher | EDP Sciences |
| Geographical Reach | international |
| ISSN | 1262-3377 |
| Volume | 14 |
| Number | 4 |
| Page Range | 780 - 794 |
| Date | 2008 |
| Abstract Text | 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. |
| Official URL | http://www.esaim-cocv.org |
| Digital Object Identifier | 10.1051/cocv:2008013 |
| Other Identification Number | merlin-id:554 |
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| Keywords | Volume constrained problems, numerical simulations, level set method, local minima |