On conormal and oblique derivative problem for elliptic equations with Dini mean oscillation coefficients
On conormal and oblique derivative problem for elliptic equations with Dini mean oscillation coefficients
复制标题
具有Dini平均振荡系数的椭圆方程的共正规和斜导数问题
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Seick Kim
中科院分区：
文献类型：
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作者：
Hongjie Dong;Jihoon Lee;Seick Kim
证明了当首项系数的平均振动满足Dini条件，低阶系数满足适当的条件，且边界由一个导数为Dini连续的C^1 $函数局部表示时，散度型椭圆型方程余法导数问题的弱解到边界是连续可微的.证明了当系数的平均振动满足Dini条件且边界局部表示为一个导数为双Dini连续的C^1 $函数时，非散度型椭圆型方程斜微商问题的强解在边界上是二次连续可微的.这特别推广了M. V. Safonov（Comm. Partial Differential Equations 20：1349- 1367，1995）
We show that weak solutions to conormal derivative problem for elliptic equations in divergence form are continuously differentiable up to the boundary provided that the mean oscillations of the leading coefficients satisfy the Dini condition, the lower order coefficients satisfy certain suitable conditions, and the boundary is locally represented by a $C^1$ function whose derivatives are Dini continuous. We also prove that strong solutions to oblique derivative problem for elliptic equations in nondivergence form are twice continuously differentiable up to the boundary if the mean oscillations of coefficients satisfy the Dini condition and the boundary is locally represented by a $C^1$ function whose derivatives are double Dini continuous. This in particular extends a result of M. V. Safonov (Comm. Partial Differential Equations 20:1349--1367, 1995)