Abstract
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.
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