A Liouville theorem for the Neumann problem of the Monge-Ampere equation

Huaiyu Jian; Xushan Tu

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arXiv · 2107.03599

A Liouville theorem for the Neumann problem of the Monge-Ampere equation

Huaiyu Jian·Xushan Tu

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Abstract

In this paper, we study the Neumann problem of Monge-Amp\`ere equations in Semi-space. For two dimensional case, we prove that its viscosity convex solutions must be a quadratic polynomial. When the space dimension $n\geq 3$, we show that the conclusion still holds if either the boundary value is zero or the viscosity convex solutions restricted on some $n-2$ dimensional subspace is bounded from above by a quadratic function.

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Huaiyu Jian, Xushan Tu. 2021-07-08. A Liouville theorem for the Neumann problem of the Monge-Ampere equation. https://arxiv.org/abs/2107.03599

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