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<p>We study the periodic homogenization problem of state-constraint Hamilton–Jacobi equations on perforated domains in the convex setting and obtain the optimal convergence rate. We then consider a dilute situation in which the diameter of the holes is much smaller than the microscopic scale. Finally, a homogenization problem with domain defects where some holes are missing is analyzed.</p>

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Quantitative Homogenization of State-Constraint Hamilton–Jacobi Equations on Perforated Domains and Applications

  • 期刊论文

  • 发表日期：

    2025年2月25日

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  • Yuxi Han,
  • Wenjia Jing,
  • Hiroyoshi Mitake,
  • Hung V. Tran

摘要

We study the periodic homogenization problem of state-constraint Hamilton–Jacobi equations on perforated domains in the convex setting and obtain the optimal convergence rate. We then consider a dilute situation in which the diameter of the holes is much smaller than the microscopic scale. Finally, a homogenization problem with domain defects where some holes are missing is analyzed.