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We consider second-order elliptic equations in nondivergence form with oblique derivative boundary conditions. We show that any strong solutions to such problems are twice continuously differentiable up to the boundary… Click to show full abstract
We consider second-order elliptic equations in nondivergence form with oblique derivative boundary conditions. We show that any strong solutions to such problems are twice continuously differentiable up to the boundary when the boundary can be locally represented by a C 1 C^1 function whose first derivatives are Dini continuous and the mean oscillations of coefficients satisfy the Dini condition. This improves a recent result by Dong, Lee, and Kim. To the best of our knowledge, such a result is new even for the Poisson equation. An extension to concave fully nonlinear elliptic equations is also presented.
Journal Title: Transactions of the American Mathematical Society
Year Published: 2020
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