Analyticity of the solutions to degenerate Monge-Ampère equations

Genggeng Huang; Yingshu Lü

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arXiv · 2012.02656

Analyticity of the solutions to degenerate Monge-Ampère equations

Genggeng Huang·Yingshu Lü

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Abstract

This paper is devoted to study the following degenerate Monge-Ampère equation: \begin{eqnarray}\label{ab1} \begin{cases} \det D^2 u=Λ_q (-u)^q \quad \text{in}\quad Ω,\\ u=0 \quad\text{on}\quad \partialΩ\end{cases} \end{eqnarray} for some positive constant $Λ_q$. Suppose $Ω\subset\subset \mathbb R^n$ is uniformly convex and analytic. Then the solution of the degenerate Monge-Ampère equation is analytic in $\barΩ$ provided $q\in \mathbb Z^+$.

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BibTeX RIS

Genggeng Huang, Yingshu Lü. 2020-12-04. Analyticity of the solutions to degenerate Monge-Ampère equations. https://arxiv.org/abs/2012.02656

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