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

Bin Deng

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

Analysis of PDEs 2019-03-14 v1

Authors: Bin Deng

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.

Keywords

Monge-Ampère equation strictly (n-1)-convex functions Neumann condition global C2 estimates continuity method existence theorem

Cite

@article{arxiv.1903.05459,
  title  = {The Monge-Amp\`ere equation for strictly $(n-1)$-convex functions with Neumann condition},
  author = {Bin Deng},
  journal= {arXiv preprint arXiv:1903.05459},
  year   = {2019}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1903.04231

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