Dolomites Research Notes on Approximation

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