We study an irregular double obstacle problem with Orlicz growth over a nonsmooth bounded domain. We establish a global Calderón–Zygmund estimate by proving that the gradient of the solution to such a nonlinear elliptic problem is as integrable as both the nonhomogeneous term in divergence form and the gradient of the associated double obstacles. We also investigate minimal regularity requirements on the relevant nonlinear operator for the desired regularity estimate.

中文翻译：

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Orlicz增长的不规则双障碍问题

我们研究了Orlicz在非光滑有界域上的不规则双障碍问题。通过证明该非线性椭圆问题的解的梯度与发散形式的非齐次项以及相关双障碍的梯度一样可积，我们建立了一个整体的Calderón–Zygmund估计。我们还研究了有关非线性算子的最小正则性要求，以获得所需的正则性估计。