Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-30T20:36:45.605Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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