We study fully nonlinear parabolic equations in nondivergence form with oblique boundary conditions. An optimal and global Calderón-Zygmund estimate is obtained by proving that the Hessian of the viscosity solution to the oblique boundary problem is as integrable as the nonhomogeneous term in $L^p$ spaces under minimal regularity requirement on the nonlinear operator, the boundary data and the boundary of the domain.

中文翻译：

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L ^{p -}斜边界条件下完全非线性抛物方程解的 Hessian 估计

我们研究了具有倾斜边界条件的非发散形式的完全非线性抛物线方程。通过证明斜边界问题的粘度解的 Hessian 与 中的非齐次项一样可积，可以获得最优的全局 Calderón-Zygmund 估计${升}^{磷}$ 非线性算子、边界数据和域边界的最小正则性要求的空间。