Typical convergence theorems for value functions and solutions of (parametric families of)
optimization problems based on È-convergence of the corresponding functionals usually
rely on equi-coercivity assumptions. Without them the connection between the È-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 ßnd limiting optimization problems (parametrized in a similar way
and determined by functionals which may diÞer from the È-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).
