Weighted Lorentz estimates for non-uniformly elliptic problems with variable exponents

In this paper, a global L ω s , t -bound for the gradient of weak solutions to non-uniformly nonlinear elliptic equations with variable exponents is presented. The main difficulties arise from variable ( p ( · ) , q ( · ) ) -growth conditions can be handled by standard techniques. Under the appropriated assumptions and minimal regularity on initial data of the problem, weighted regularity estimates in the frame of Lorentz spaces will be established. Furthermore, the use of level-set inequalities on distribution functions is also imposed to obtained the norm bounds in a wide range of generalized Lebesgue spaces such as Lorentz, Lorentz-Morrey or Orlicz spaces, etc.