  We consider a class of integral functionals with convex integrand with
respect to the gradient variable, assuming that the function that measures the
oscillation of the integrand with respect to the x variable belongs to a
suitable Sobolev space W^{1;q}. We prove a result of higer differentiability
for the minimizers. We also infer a result of Lipschitz regularity of
minimizers if q > n, and a result of higher integrability for the gradient if q
= n. The novelty here is that we deal with integrands satisfying subquadratic
growth conditions with respect to gradient variable.
