A new partial regularity result for non-autonomous convex integrals with non-standard growth conditions

We establish C1,γC1,γ-partial regularity of minimizers of non-autono-mous convex integral functionals of the type: F(u;Ω):=∫Ωf(x,Du)dx, with non-standard growth conditions into the gradient variable1L|ξ|p⩽f(x,ξ)⩽L(1+|ξ|q) for a couple of exponents p,qp,q such that1