| Issue |
ESAIM: COCV
Volume 10, Number 1, January 2004
|
|
|---|---|---|
| Page(s) | 84 - 98 | |
| DOI | https://doi.org/10.1051/cocv:2003034 | |
| Published online | 15 February 2004 | |
Abstract variational problems with volume constraints
Center for Nonlinear Analysis, Carnegie Mellon University, 5000 Forbes Av., Pittsburgh, PA 15213, USA; rieger@andrew.cmu.edu.
Received:
25
March
2002
Revised:
25
July
2002
Revised:
3
April
2003
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.
Mathematics Subject Classification: 49
Key words: Level set constraints / nonconvex problems / minimization.
© EDP Sciences, SMAI, 2004
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