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 -limit argument and illustrate this with numerical computations. Finally we construct explicitly local and global minimizers for problems with two volume constraints.
Mots clés : volume constrained problems, numerical simulations, level set method, local minima
@article{COCV_2008__14_4_780_0, author = {Oudet, \'Edouard and Rieger, Marc Oliver}, 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}, mrnumber = {2451796}, zbl = {1148.49030}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2008013/} }
TY - JOUR AU - Oudet, Édouard AU - Rieger, Marc Oliver TI - Local minimizers of functionals with multiple volume constraints JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 SP - 780 EP - 794 VL - 14 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2008013/ DO - 10.1051/cocv:2008013 LA - en ID - COCV_2008__14_4_780_0 ER -
%0 Journal Article %A Oudet, Édouard %A Rieger, Marc Oliver %T Local minimizers of functionals with multiple volume constraints %J ESAIM: Control, Optimisation and Calculus of Variations %D 2008 %P 780-794 %V 14 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2008013/ %R 10.1051/cocv:2008013 %G en %F COCV_2008__14_4_780_0
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. http://www.numdam.org/articles/10.1051/cocv:2008013/
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