Calderón-Zygmund estimates for higher order elliptic equations in Orlicz-Sobolev spaces

In this paper we obtain Calderón-Zygmund estimates for the laplacian of the following fourth order quasilinear elliptic problem $$\mathrm{\Delta }(g(\mathrm{\Delta }u)\mathrm{\Delta }u)=\mathrm{\Delta }(g(\mathrm{\Delta }f)\mathrm{\Delta }f)\mathrm{.}$$ where the primitive of $g(t)t$, $G(t)$, is an $N-$function. We prove that if $G(f)\in L^q$, then $G(\mathrm{\Delta }u)\in L^q$ for $q\ge 1$.