Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 39, pp. 1-16.

Title: Boundary regularity for nondivergence elliptic equation with unbounded drift

Authors: Yongpan Huang (Xi'an Jiaotong Univ., Xi'an, China)
         Qiaozhu Zhai  (Xi'an Jiaotong Univ., Xi'an, China)
         Shulin Zhou   (Xi'an Jiaotong Univ., Xi'an, China)
 
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.