SIAM Journal on Mathematical Analysis, Volume 52, Issue 5, Page 4161-4184, January 2020.
We study state-constraint static Hamilton--Jacobi equations in a sequence of domains $\{\Omega_k\}_{k \in \Bbb{N}}$ in $\Bbb{R}^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k\in \Bbb{N}$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega = \bigcup_{k \in \Bbb{N}} \Omega_k$. In many cases, the rates obtained are proven to be optimal. Various new examples and discussions are provided at the end of the paper.

中文翻译：

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嵌套域中的状态约束静态Hamilton--Jacobi方程

SIAM数学分析杂志，第52卷，第5期，第4161-4184页，2020年1月。
我们在一系列域$ \ {\ Omega_k \} _ {k \ in \ Bbb中研究状态约束静态汉密尔顿-雅各比方程$ \ Bbb {R} ^ n $中的{N}} $，使得\ Bbb {N} $中所有$ k \ $ Omega_k \ subset \ Omega_ {k + 1} $。我们获得收敛速度$ u_k $（$ \ Omega_k $中的状态约束问题的解）到$ u $（$ \ Omega = \ bigcup_ {k \ in \ Bbb {N中的问题）的解}} \ Omega_k $。在许多情况下，事实证明获得的速率是最佳的。本文末尾提供了各种新示例和讨论。