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

Abstract

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 $(p\left(x\right),q\left(x\right))$-growth condition and $(\delta ,R)$-BMO condition, while the exponents $p\left(x\right),q\left(x\right)$ are strong $log$-Hölder continuous functions. The approach of this paper is mainly based on the perturbation technique and maximal function free technique.