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.

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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