TY - JOUR
T1 - The Monge-Ampère Equation for Strictly $(n−1)$-Convex Functions with Neumann Condition
AU - Deng , Bin
JO - Journal of Mathematical Study
VL - 1
SP - 66
EP - 89
PY - 2020
DA - 2020/03
SN - 53
DO - http://doi.org/10.4208/jms.v53n1.20.04
UR - https://global-sci.org/intro/article_detail/jms/15208.html
KW - Neumann problem, $(n−1)$-convex, elliptic equation.
AB - <p style="text-align: justify;">A $C^2$ function on $\mathbb{R}^n$ is called strictly $(n-1)$-convex if the sum of any $n-1$ eigenvalues of its Hessian is positive. In this paper, we establish a global $C^2$ estimates to the Monge-Ampère equation for strictly $(n-1)$-convex functions with Neumann condition. By the method of continuity, we prove an existence theorem for strictly $(n-1)$-convex solutions of the Neumann problems.</p>