In this talk, we will discuss weighted Lq, 1<q<2, estimates for nonlinear elliptic equations,

as an application of Lp estimates, 1<p<∞, for linear ellitpic equations.

We will assume that the nonlinearity A(x,ξ) satisfies linear growth condtions

and that $A(x, \xi)$ is asymptotically Uhlenbeck, i.e., |A(x,ξ)−A(x)ξ|≤ϵ|ξ|

for sufficiently large |ξ|.