Regularity for minimizers of integrals with nonstandard growth

We deal with variational integrals ∫Ωf(x,Du(x))dx∫Ωf(x,Du(x))dx and we consider a minimizer u:Ω⊂Rn→Ru:Ω⊂Rn→R among all functions that agree on the boundary ∂Ω∂Ω with some fixed boundary value u∗u∗. We assume that the boundary datum u∗u∗ makes the density f(x,Du∗(x))f(x,Du∗(x)) more integrable and we prove that the minimizer uu enjoy higher integrability.