Abstract variational problems with volume constraints

Marc Oliver Rieger

ESAIM: Control, Optimisation and Calculus of Variations (2010)

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

Abstract

top
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

top

Rieger, Marc Oliver. "Abstract variational problems with volume constraints." ESAIM: Control, Optimisation and Calculus of Variations 10.1 (2010): 84-98. <http://eudml.org/doc/90722>.

@article{Rieger2010,
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.; level set constraints; minimization},
language = {eng},
month = {3},
number = {1},
pages = {84-98},
publisher = {EDP Sciences},
title = {Abstract variational problems with volume constraints},
url = {http://eudml.org/doc/90722},
volume = {10},
year = {2010},
}

TY - JOUR
AU - Rieger, Marc Oliver
TI - Abstract variational problems with volume constraints
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
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.; level set constraints; minimization
UR - http://eudml.org/doc/90722
ER -

References

top
  1. L. Ambrosio, I. Fonseca, P. Marcellini and L. Tartar, On a volume-constrained variational problem. Arch. Rational Mech. Anal.149 (1999) 23-47.  Zbl0945.49005
  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.  Zbl0857.76008
  3. M. Morini and M.O. Rieger, On a volume constrained variational problem with lower order terms. Appl. Math. Optim (to appear).  Zbl1042.49014
  4. S. Mosconi and P. Tilli, Variational problems with several volume constraints on the level sets. Calc. Var. Partial Differential Equations14 (2002) 233-247.  Zbl0995.49003
  5. P. Tilli, On a constrained variational problem with an arbitrary number of free boundaries. Interfaces Free Bound.2 (2000) 201-212.  Zbl0995.49002

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.