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Abstract variational problems with volume constraints

Published online by Cambridge University Press:  15 February 2004

Marc Oliver Rieger
Marc Oliver Rieger*
Affiliation:
Center for Nonlinear Analysis, Carnegie Mellon University, 5000 Forbes Av., Pittsburgh, PA 15213, USA; rieger@andrew.cmu.edu.
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Abstract

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.

Keywords

Level set constraintsnonconvex problemsminimization.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 1 , January 2004 , pp. 84 - 98
Copyright
© EDP Sciences, SMAI, 2004

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References

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