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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

Ambrosio, L., Fonseca, I., Marcellini, P. and Tartar, L., On a volume-constrained variational problem. Arch. Rational Mech. Anal. 149 (1999) 23-47. CrossRef
Gurtin, M.E., Polignone, D. and Vinals, J., Two-phase binary fluids and immissible fluids described by an order parameter. Math. Models Methods Appl. Sci. 6 (1996) 815-831. CrossRef
M. Morini and M.O. Rieger, On a volume constrained variational problem with lower order terms. Appl. Math. Optim (to appear).
Mosconi, S. and Tilli, P., Variational problems with several volume constraints on the level sets. Calc. Var. Partial Differential Equations 14 (2002) 233-247. CrossRef
Tilli, P., On a constrained variational problem with an arbitrary number of free boundaries. Interfaces Free Bound. 2 (2000) 201-212. CrossRef