Weighted Lorentz estimates with a variable power for non-uniformly elliptic two-sided obstacle problems

We proved an optimal local Calderón–Zygmund type estimate with a variable power in weighted Lorentz spaces for the weak solution of non-uniformly elliptic two-sided obstacle problems. It is mainly assumed that the nonlinearity satisfies the (p(x),q(x))-growth condition and (δ,R)-BMO condition, while the exponents p(x),q(x) are strong log-Hölder continuous functions. The approach of this paper is mainly based on the perturbation technique and maximal function free technique.