Limit Behavior of Complex Special Lagrangian Equations With Neumann Boundary-Value Conditions
Limit Behavior of Complex Special Lagrangian Equations With Neumann Boundary-Value Conditions
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DOI：
10.1093/imrn/rnaa378
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发表时间：
2021-02
影响因子：
1
通讯作者：
Xiaoling Han;Xishen Jin
中科院分区：
文献类型：
--
作者：
Xiaoling Han;Xishen Jin
我们考虑区域$\Omega\subset\mathbb{C}^{n}$上具有Neumann边界条件的复杂特殊拉格朗日方程：$$\Begin{Align*}&\Left\\Begin{ARRAY}{ll}{\sum\Limits_{i=1}^n\arctan k\lambda_{i}(H(u_{k，\varepsilon}))=\theta_k(Z)}&{\tExm{in}\Omega}\\{D_{\nu}{u_{k，\varepsilon}=-\varepsilon{u_{k，\varepsilon}}+\varphi(Z)}&{\tExtrm{on}\Partial\Omega}\end{ARRAY}\Right..我们证明了这些方程的全局一致估计。作为$k，我们证明了$u_(k，varepsilon)$在$\Omega$上收敛于具有相同Neumann边界条件的$J_$型方程的解。
We consider the following complex special Lagrangian equations with Neumann boundary conditions on a domain $\Omega \subset \mathbb{C}^{n} $: $$\begin{align*}& \left\{\begin{array}{ll} {\sum\limits_{i=1}^n \arctan k \lambda_{i} (H(u_{k,\varepsilon} ))=\Theta_k(z)} & {\textrm{ in } \Omega} \\{D_{\nu} {u_{k,\varepsilon }}=-\varepsilon{u_{k,\varepsilon }}+\varphi(z)} & {\textrm{ on } \partial \Omega}\end{array}\right.. \end{align*}$$We prove uniform global estimates for these equations. As $k\to +\infty $, we prove that $u_{ k,\varepsilon }$ converges to the solution of $J$-type equation with the same Neumann boundary condition on $\Omega $.