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

We establish C 1,γ -partial regularity of minimizers of non autonomous convex integral functionals of the type: F(u; Ω) :=´Ω f (x, Du) dx, with non standard growth conditions into the gradient for a couple of exponents p, q such that and α-Hölder continuous dependence with respect to the x variable. The significant point here is that the distance between the exponents p and q is independent of α. Moreover this bound on the gap between the growth and the coercitivity exponents improves previous results in this setting