Open AccessClassical solutions of oblique derivative problem in nonsmooth domains with mean Dini coefficients
Author(s) -
Hongjie Dong,
Zongyuan Li
Publication year - 2020
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/tran/8042
Subject(s) - mathematics , oblique case , differentiable function , boundary (topology) , elliptic curve , mathematical analysis , function (biology) , derivative (finance) , algorithm , philosophy , linguistics , evolutionary biology , biology , financial economics , economics
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.