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

Abstract:
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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