Abstract variational problems with volume constraints

Marc Oliver Rieger

ESAIM: Control, Optimisation and Calculus of Variations (2004)

  • Volume: 10, Issue: 1, page 84-98
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Rieger, Marc Oliver. "Abstract variational problems with volume constraints." ESAIM: Control, Optimisation and Calculus of Variations 10.1 (2004): 84-98. <http://eudml.org/doc/245752>.

@article{Rieger2004,
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.},
author = {Rieger, Marc Oliver},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {level set constraints; nonconvex problems; minimization},
language = {eng},
number = {1},
pages = {84-98},
publisher = {EDP-Sciences},
title = {Abstract variational problems with volume constraints},
url = {http://eudml.org/doc/245752},
volume = {10},
year = {2004},
}

TY - JOUR
AU - Rieger, Marc Oliver
TI - Abstract variational problems with volume constraints
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2004
PB - EDP-Sciences
VL - 10
IS - 1
SP - 84
EP - 98
AB - 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.
LA - eng
KW - level set constraints; nonconvex problems; minimization
UR - http://eudml.org/doc/245752
ER -

References

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  1. [1] L. Ambrosio, I. Fonseca, P. Marcellini and L. Tartar, On a volume-constrained variational problem. Arch. Rational Mech. Anal. 149 (1999) 23-47. Zbl0945.49005MR1723033
  2. [2] M.E. Gurtin, D. Polignone and J. Vinals, Two-phase binary fluids and immissible fluids described by an order parameter. Math. Models Methods Appl. Sci. 6 (1996) 815-831. Zbl0857.76008MR1404829
  3. [3] M. Morini and M.O. Rieger, On a volume constrained variational problem with lower order terms. Appl. Math. Optim (to appear). Zbl1042.49014MR1977877
  4. [4] S. Mosconi and P. Tilli, Variational problems with several volume constraints on the level sets. Calc. Var. Partial Differential Equations 14 (2002) 233-247. Zbl0995.49003MR1890401
  5. [5] P. Tilli, On a constrained variational problem with an arbitrary number of free boundaries. Interfaces Free Bound. 2 (2000) 201-212. Zbl0995.49002MR1760412

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