The aim of this article is to study partial regularity of a minimizer u: Ω ⊂ Rn → RN for a double phase functional with variable exponents: ∫ (||Du||Ap(x) + a(x) ||Du||Aq(x)) dx, where || . || stands for the norm deduced from a positive definite sufficiently continuoustensor field A:=(Aijαβ(x,u)) ( (x,u) ∈ Ω × RN). We show that a minimizer u is in the class C1,γ(Ω1;RN ) for some constant γ ∈ (0,1) and open subset Ω1 ⊂ Ω . We obtain also an estimate for the Hausdorff dimension of Ω \ Ω1.
MSC Classification: 35J20 , 35J47 , 35J60 , 49N60