Abstract In this paper, we consider the solutions of the non-homogeneous quasilinear elliptic obstacle problems involving measure data. At first we prove the existence of approximable solutions to these problems. Then we establish pointwise and oscillation estimates for the gradients of solutions via the nonlinear Wolff potentials, and these yield results on C 1 , α -regularity of solutions.

中文翻译：

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椭圆障碍问题的梯度势估计

摘要 在本文中，我们考虑了涉及测量数据的非齐次拟线性椭圆障碍问题的解。首先我们证明这些问题的近似解是存在的。然后我们通过非线性沃尔夫势建立解梯度的逐点和振荡估计，这些产生关于 C 1 ，α -解的正则性的结果。