The Monge-Ampère Equation for Strictly $(n−1)$-Convex Functions with Neumann Condition

The Monge-Ampère Equation for Strictly $(n−1)$-Convex Functions with Neumann Condition

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.

Author Details

Bin Deng