Abstract variational problems with volume constraints
ESAIM: Control, Optimisation and Calculus of Variations, Volume 10 (2004) no. 1, p. 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 : https://doi.org/10.1051/cocv:2003034
Classification:  49
Keywords: level set constraints, nonconvex problems, minimization
@article{COCV_2004__10_1_84_0,
     author = {Rieger, Marc Oliver},
     title = {Abstract variational problems with volume constraints},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {10},
     number = {1},
     year = {2004},
     pages = {84-98},
     doi = {10.1051/cocv:2003034},
     zbl = {1068.49002},
     mrnumber = {2084256},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2004__10_1_84_0}
}
Rieger, Marc Oliver. Abstract variational problems with volume constraints. ESAIM: Control, Optimisation and Calculus of Variations, Volume 10 (2004) no. 1, pp. 84-98. doi : 10.1051/cocv:2003034. http://www.numdam.org/item/COCV_2004__10_1_84_0/

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