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nonconvex problems

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Abstract variational problems with volume constraints
Marc Oliver Rieger
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 10 / Issue 1 / January 2004

Published online by Cambridge University Press:

15 February 2004, pp. 84-98

Print publication:

January 2004
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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.