Geodesic
Local minimizers of functionals with multiple volume constraints
ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 780-794

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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.

DOI : 10.1051/cocv:2008013
Classification : 49J, 65K10
Keywords: volume constrained problems, numerical simulations, level set method, local minima 
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     title = {Local minimizers of functionals with multiple volume constraints},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {780--794},
     publisher = {EDP-Sciences},
     volume = {14},
     number = {4},
     year = {2008},
     doi = {10.1051/cocv:2008013},
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     zbl = {1148.49030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008013/}
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Oudet, Édouard; Rieger, Marc Oliver. Local minimizers of functionals with multiple volume constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 780-794. doi: 10.1051/cocv:2008013

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