
Journal of Convex Analysis 09 (2002), No. 2, 439462 Copyright Heldermann Verlag 2002 On Limits of Variational Problems. The Case of a NonCoercive Functional Lorenzo Freddi Dip. di Matematica e Informatica, Università di Udine, via delle Scienze 206, 33100 Udine, Italy freddi@dimi.uniud.it Alexander D. Ioffe Dept. of Mathematics, Technion, Haifa 32000, Israel ioffe@math.technion.ac.il Typical convergence theorems for value functions and solutions of (parametric families of) optimization problems based on Gammaconvergence of the corresponding functionals usually rely on equicoercivity assumptions. Without them the connection between the Gammalimit 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 coercivitytype assumption, to find limiting optimization problems (parametrized in a similar way and determined by functionals which may differ from the Gammalimits 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). [ Fulltextpdf (544 KB)] 