Abstract: We consider
the problem of minimizing autonomous, multiple
integrals like
where
f
: R´RN®
[0, ¥)
is a continuous,
possibly nonconvex function of the gradient
variable
Ñu.We discuss examples
where the minimum is not attained, comment on
the main results on this subject and sketch
the proof of a quite general existence result
recently obtained by the authors. Eventually,
we discuss some open problems and possible
directions of research in this field.
Keywords and phrases: nonconvex variational problems, existence of minimizers, convex integration.
