Weighted gradient estimates for general nonlinear elliptic equations involving measure data

Abstract

We prove a global Calderón-Zygmund type estimate in the weighted Lorentz spaces for the gradients of solution to general nonlinear elliptic equations involving a signed Radon measure. The associated nonlinearity is assumed to depend on the solution itself and satisfy the (δ,R0)-BMO condition with respect to x-variable, while the boundary of underlying domain is assumed to be Reifenberg flat. Here, we mainly employ the perturbation technique, the modified Vitali type covering and an extrapolation argument. As its direct consequence, we also prove global gradient estimates in the Orlicz spaces and variable Lebesgue spaces, respectively.