Regularity for solutions to a class of PDE’s with Orlicz growth

We consider weak solutions u : Ω→R to partial differential equations of the formdiv a(x, Du) = 0in Ω ⊂ Rn, n > 2, where the partial map x 7→ a(x,ξ) has a suitable Sobolev regularity and satisfiesgrowth conditions with respect to the second variable expressed through an Orlicz function φ . We provethe second order regularity of the weak solutions.