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Gradient estimates for Neumann boundary value problem of Monge–Ampère type equations

Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, P. R. China

College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210094, P. R. China

E-mail Address: jiangfeida@math.tsinghua.edu.cn

E-mail Address: jfd2001@163.com

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Ni Xiang

Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, P. R. China

E-mail Address: nixiang@hubu.edu.cn

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, and

Jinju Xu

Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China

E-mail Address: jjxujane@shu.edu.cn

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https://doi.org/10.1142/S0219199716500413Cited by:2 (Source: Crossref)

Abstract

This paper concerns the gradient estimates for Neumann problem of a certain Monge–Ampère type equation with a lower order symmetric matrix function in the determinant. Under a one-sided quadratic structure condition on the matrix function, we present two alternative full discussions of the global gradient bound for the elliptic solutions.

Keywords:

AMSC: 35J66, 35J96

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