  It is studied the lower semicontinuity of functionals of the type
$\int_\Omega f(x,u,v, \nabla u)dx$ with respect to the $(W^{1,1}\times
L^p)$-weak \ast topology. Moreover in absence of lower semicontinuity, it is
also provided an integral representation in $W^{1,1} \times L^p$ for the lower
semicontinuous envelope.
