Integral representation for a class of C 1 -convex functionals
Abstract
In view of the applications to the asymptotic analysis of a family of obstacle problems, we consider a class of convex local functionals
F(u,A)
, defined for all functions
u
in a suitable vector valued Sobolev space and for all open sets
A
in
R
n
. Sufficient conditions are given in order to obtain an integral representation of the form
F(u,A)=
∫
A
f(x,u(x))dμ+ν(A)
, where
μ
and
ν
are Borel measures and
f
is convex in the second variable.