The Monge-Amp\`ere equation for strictly $(n-1)$-convex functions with Neumann condition

Bin Deng

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arXiv · 1903.05459

The Monge-Amp\`ere equation for strictly $(n-1)$-convex functions with Neumann condition

Bin Deng

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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-Amp\`ere 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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Bin Deng. 2019-03-11. The Monge-Amp\`ere equation for strictly $(n-1)$-convex functions with Neumann condition. https://arxiv.org/abs/1903.05459

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