Abstract variational problems with volume constraints
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 1, pp. 84-98.

Existence results for a class of one-dimensional abstract variational problems with volume constraints are established. The main assumptions on their energy are additivity, translation invariance and solvability of a transition problem. These general results yield existence results for nonconvex problems. A counterexample shows that a naive extension to higher dimensional situations in general fails.

DOI : 10.1051/cocv:2003034
Classification : 49
Mots-clés : level set constraints, nonconvex problems, minimization 
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     title = {Abstract variational problems with volume constraints},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {84--98},
     publisher = {EDP-Sciences},
     volume = {10},
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     doi = {10.1051/cocv:2003034},
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     url = {http://www.numdam.org/articles/10.1051/cocv:2003034/}
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Rieger, Marc Oliver. Abstract variational problems with volume constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 1, pp. 84-98. doi : 10.1051/cocv:2003034. http://www.numdam.org/articles/10.1051/cocv:2003034/

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