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State-constraint static Hamilton-Jacobi equations in nested domains. (English) Zbl 1448.35103

Summary: 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 \(k\in \mathbb{N} \). 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.

MSC:

35F21 Hamilton-Jacobi equations
35B40 Asymptotic behavior of solutions to PDEs
35D40 Viscosity solutions to PDEs
49J20 Existence theories for optimal control problems involving partial differential equations
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
70H20 Hamilton-Jacobi equations in mechanics
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