Electron. J. Differential Equations, Vol. 2019 (2019), No. 39, pp. 1-16.

Boundary regularity for nondivergence elliptic equation with unbounded drift

Yongpan Huang, Qiaozhu Zhai, Shulin Zhou

We obtain the pointwise boundary differentiability of strong solutions for elliptic equations with the lower order coefficients, the boundary, and the right-hand side term satisfying a Dini type condition. Furthermore, we establish a pointwise estimate of strong solutions and show that the gradients of the strong solutions are continuous along the boundary if the drift term, the boundary, and the right-hand side term satisfy a uniform Dini type condition on the boundary.

Submitted March 27, 2018. Published March 12, 2019.
Math Subject Classifications: 35J25, 35B65,
Key Words: Elliptic equations; strong Solutions; unbounded drift; boundary regularity.

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Yongpan Huang
Department of Mathematics
Xi'an Polytechnic University
Xi'an 710048, China
email: yongpanhuang@xjtu.edu.cn, huangyongpan@gmail.com
Qiaozhu Zhai
Systems Engineering Institute
Xi'an Jiaotong University
Xi'an 710049, China
email: qzzhai@sei.xjtu.edu.cn
Shulin Zhou
School of Mathematical Sciences
Peking University
Beijing, 100871, China
email: szhou@math.pku.edu.cn

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