Journal of Convex Analysis 09 (2002), No. 2, 439--462
Copyright Heldermann Verlag 2002
On Limits of Variational Problems. The Case of a Non-Coercive 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 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).
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