Gradient estimates for the p-laplace equation with a singular source

In this paper we will employ the method of "DeGiorgi-Nash-Moser" to establish a L-infinity local estimate for the gradient of local weak solutions to p-Laplacian equation -div|del u|(p-2)del u = f(x,u,del u). (1.1) In this work we extend to 1<p< 2 the local estimates of the & Vert;del u & Vert;(infinity )of the local weak solutions of (1.1), obtained by Bhattacharya, DiBenedetto and Manfrediin Limits as p ->infinity of Delta(p)u(p)=f and related extremal problems(1989), for p>2.