Geodesic
On Limits of Variational Problems. The Case of a Non-Coercive Functional
Journal of convex analysis, Tome 9 (2002) no. 2, pp. 439-462

Voir la notice de l'article provenant de la source Heldermann Verlag

Typical convergence theorems for value functions and solutions of (parametric families of) optimization problems based on Gamma-convergence of the corresponding functionals usually rely on equi-coercivity assumptions. Without them the connection between the Gamma-limit of the functionals and values and/or solutions of the problems may be completely broken. The question to be discussed is whether it is possible, even in the absence of a coercivity-type assumption, to find limiting optimization problems (parametrized in a similar way and determined by functionals which may differ from the Gamma-limits of the functionals of the sequence) such that the value functions and solutions of the problems of the sequence converge in a certain sense to those of the limiting problems. A positive answer to the question is given to a class of variational problems (containing optimal control problems with linear dynamics). 
@article{JCA_2002_9_2_JCA_2002_9_2_a7,
     author = {L. Freddi and A. D. Ioffe},
     title = {On {Limits} of {Variational} {Problems.} {The} {Case} of a {Non-Coercive} {Functional}},
     journal = {Journal of convex analysis},
     pages = {439--462},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2002},
     url = {http://geodesic.mathdoc.fr/item/JCA_2002_9_2_JCA_2002_9_2_a7/}
}
TY  - JOUR
AU  - L. Freddi
AU  - A. D. Ioffe
TI  - On Limits of Variational Problems. The Case of a Non-Coercive Functional
JO  - Journal of convex analysis
PY  - 2002
SP  - 439
EP  - 462
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCA_2002_9_2_JCA_2002_9_2_a7/
ID  - JCA_2002_9_2_JCA_2002_9_2_a7
ER  - 
%0 Journal Article
%A L. Freddi
%A A. D. Ioffe
%T On Limits of Variational Problems. The Case of a Non-Coercive Functional
%J Journal of convex analysis
%D 2002
%P 439-462
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCA_2002_9_2_JCA_2002_9_2_a7/
%F JCA_2002_9_2_JCA_2002_9_2_a7
L. Freddi; A. D. Ioffe. On Limits of Variational Problems. The Case of a Non-Coercive Functional. Journal of convex analysis, Tome 9 (2002) no. 2, pp. 439-462. http://geodesic.mathdoc.fr/item/JCA_2002_9_2_JCA_2002_9_2_a7/