Gradient estimates for nonlinear elliptic double obstacle problems

We study a nonlinear elliptic double obstacle problem with irregular data and establish an optimal Calderón–Zygmund theory. The partial differential operator is of the p-Laplacian type and includes merely measurable coefficients in one variable. We prove that the gradient of a weak solution is as integrable as both the gradient of assigned two obstacles and the nonhomogeneous divergence term under a small BMO semi-norm assumption on the coefficients in the other variables.