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

We establish C1,γ-partial regularity of minimizers of non-autono-mous convex integral functionals of the type: , with non-standard growth conditions into the gradient variable 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.