论文标题
解析元素方程的解决方案的分析性
Analyticity of the solutions to degenerate Monge-Ampère equations
论文作者
论文摘要
本文专门研究以下退化的monge-ampère方程：\ begin {eqnarray} \ label {ab1} \ begin {cases} \ det d^2 u =λ_q（-u） \partialΩ\ end {cases} \ end {eqnarray}对于某些正常数$λ_q$。假设$ω\ subset \ subset \ mathbb r^n $均匀凸和分析。然后，在\ mathbb z^+$中提供了$ \barΩ$中的退化monge-ampère方程的解决方案。
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 $q\in \mathbb Z^+$.
