Weighted gradient estimates for the class of very singular p-Laplace system

Abstract

Let n∈{2,3,4,…}, N∈{1,2,3,…} and [Formula presented]. Let β∈(1,∞) be such that [Formula presented] and f∈Lβ(Rn,RN). Consider the p-Laplace system −Δpu=−div(|Du|p−2Du)=finRn. We obtain a weighted gradient estimate for weak solutions of this system.