Weighted variable exponent Sobolev estimates for elliptic equations with non-standard growth and measure data

Consider the following nonlinear elliptic equation of p(x)-Laplacian type with nonstandard growth where is a Reifenberg domain in , is a Radon measure defined on with finite total mass and the nonlinearity is modeled upon the -Laplacian. We prove the estimates on weighted variable exponent Lebesgue spaces for gradients of solutions to this equation in terms of Muckenhoupt-Wheeden type estimates. As a consequence, we obtain some new results such as the weighted regularity (with constants ) and estimates on Morrey spaces for gradients of the solutions to this non-linear equation.