Abstract variational problems with volume constraints
Center for Nonlinear Analysis, Carnegie Mellon University, 5000 Forbes Av., Pittsburgh, PA 15213, USA; email@example.com.
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