Partial regularity for minimizers of a class of non autonomous functionals with nonstandard growth

We study the regularity of the local minimizers of non autonomous integral functionals of the type (Formula Presented.)where Φ is an Orlicz function satisfying both the Δ2 and the ∇ 2 conditions, p(x) : Ω⊂ Rn→ (1 , + ∞) is continuous and the function A(x,s)=(Aijαβ(x,s)) is uniformly continuous. More precisely, under suitable assumptions on the functions Φ and p(x), we prove the Hölder continuity of the minimizers. Moreover, assuming in addition that the function A(x,s)=(Aijαβ(x,s)) is Hölder continuous, we prove the partial Hölder continuity of the gradient of the local minimizers too. © 2017, Springer-Verlag GmbH Germany.