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<p>In this paper, we study a quantitative refinement of a classical symmetrisation result for first-order Hamilton-Jacobi equations. We prove that the deficit in the comparison result, established by Giarrusso and Nunziante, controls both the asymmetry of the domain and the deviation of the solution and data from radial symmetry. This yields a stability version of the Giarrusso-Nunziante inequality.</p>

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Quantitative Comparison Results for First-Order Hamilton-Jacobi Equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月15日

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  • Vincenzo Amato,
  • Luca Barbato

摘要

In this paper, we study a quantitative refinement of a classical symmetrisation result for first-order Hamilton-Jacobi equations. We prove that the deficit in the comparison result, established by Giarrusso and Nunziante, controls both the asymmetry of the domain and the deviation of the solution and data from radial symmetry. This yields a stability version of the Giarrusso-Nunziante inequality.