Regularity theory for quasilinear elliptic equations of p-Schrödinger type with certain potentials

Abstract

In this paper we study the regularity theory in Orlicz spaces for the following divergence quasilinear elliptic equations of p-Schr?dinger type with certain potentials in the whole space Rn under some proper conditions ?div(|?u|p?2?u)+ V(x)|u|p?2 u = ?div(|f|p?2 f). Especially when p = 2, the above equation can be reduced to the classical linear divergence elliptic Schr?dinger equation ??u + V(x)u = ?div f. Moreover, we would like to remark that the results in this work generalize the results of our previous paper [50].