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

Abstract

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

20 pages, submitted