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تسجيل مستخدم جديدState-constraint static Hamilton-Jacobi equations in nested domains
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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.
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Let $(Omega, mu)$ be a probability space endowed with an ergodic action, $tau$ of $( {mathbb R} ^n, +)$. Let $H(x,p; omega)=H_omega(x,p)$ be a smooth Hamiltonian on $T^* {mathbb R} ^n$ parametrized by $omegain Omega$ and such that $ H(a+x,p;tau_aomeg
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