State-constraint static Hamilton-Jacobi equations in nested domains

We study state-constraint static Hamilton-Jacobi equations in a sequence of domains ${Omega_k}_{k in mathbb{N}}$ in $mathbb{R}^n$ such that $Omega_k subset Omega_{k+1}$ for all $kin mathbb{N}$. 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 $Omega = bigcup_{k in mathbb{N}} Omega_k$. In many cases, the rates obtained are proven to be optimal. Various new examples and discussions are provided at the end of the paper.