Year: 2020
Author: Bin Deng
Journal of Mathematical Study, Vol. 53 (2020), Iss. 1 : pp. 66–89
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v53n1.20.04
Journal of Mathematical Study, Vol. 53 (2020), Iss. 1 : pp. 66–89
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Neumann problem $(n−1)$-convex elliptic equation.