Pointwise gradient estimates for a class of singular quasilinear equations with measure data

摘要

Local and global pointwise gradient estimates are obtained for solutions to the quasilinear elliptic equation with measure data - div(A(x, del u)) = mu in a bounded and possibly nonsmooth domain Omega in R-n. Here div(A(x, del u)) is modeled after the p-Laplacian. Our results extend earlier known results to the singular case in which 3n-2/2n-1 < p <= 2 - 1/n (C) 2019 Published by Elsevier Inc.