In this paper, we study the global $C^{1, 1}$ regularity for viscosity solution of the degenerate Monge–Ampère type equation $\det [D^{2}u-A(x, Du)]=B(x, u, Du)$ with the Neumann boundary value condition $D_{\nu }u=\varphi (x)$ , where the matrix A is under the regular condition and some structure conditions, and the right-hand term B is nonnegative.

中文翻译：

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退化Monge-Ampère型方程的Neumann问题

在本文中，我们研究了退化Monge–Ampère型方程$ \ det [D ^ {2} uA（x，Du）] = B（x，的粘性解的整体$ C ^ {1，1} $正则性。 u，Du）$，其中Neumann边值条件为$ D _ {\ nu} u = \ varphi（x）$，其中矩阵A在规则条件和某些结构条件下，而右手项B为非负值。