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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.
@article{COCV_2004__10_1_84_0,
author = {Rieger, Marc Oliver},
title = {Abstract variational problems with volume constraints},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {84--98},
publisher = {EDP-Sciences},
volume = {10},
number = {1},
year = {2004},
doi = {10.1051/cocv:2003034},
mrnumber = {2084256},
zbl = {1068.49002},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003034/}
}
TY - JOUR AU - Rieger, Marc Oliver TI - Abstract variational problems with volume constraints JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2004 SP - 84 EP - 98 VL - 10 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003034/ DO - 10.1051/cocv:2003034 LA - en ID - COCV_2004__10_1_84_0 ER -
%0 Journal Article %A Rieger, Marc Oliver %T Abstract variational problems with volume constraints %J ESAIM: Control, Optimisation and Calculus of Variations %D 2004 %P 84-98 %V 10 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003034/ %R 10.1051/cocv:2003034 %G en %F COCV_2004__10_1_84_0
Rieger, Marc Oliver. Abstract variational problems with volume constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 1, pp. 84-98. doi: 10.1051/cocv:2003034
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