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Zbl 1068.49002
Rieger, Marc Oliver
Abstract variational problems with volume constraints. (English)
[J] ESAIM, Control Optim. Calc. Var. 10, 84-98 (2004). ISSN 1292-8119; ISSN 1262-3377/e

Summary: 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.
MSC 2000:
*49J27 Optimal control problems in abstract spaces (existence)
49J10 Free problems in several independent variables (existence)

Keywords: level set constraints; nonconvex problems; minimization

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