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<p>We establish a new sharp estimate of the order of the vanishing of solutions to parabolic equations with variable coefficients. For real-analytic leading coefficients, we prove a localised estimate of the nodal set, at a given time-level, that generalises the celebrated one of Donnelly and Fefferman. We also establish Landis type results for global solutions.</p>

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Sharp Order of Vanishing for Parabolic Equations, Nodal Set Estimates and Landis Type Results

  • 期刊论文

  • 发表日期：

    2025年11月2日

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  • Vedansh Arya,
  • Agnid Banerjee,
  • Nicola Garofalo

摘要

We establish a new sharp estimate of the order of the vanishing of solutions to parabolic equations with variable coefficients. For real-analytic leading coefficients, we prove a localised estimate of the nodal set, at a given time-level, that generalises the celebrated one of Donnelly and Fefferman. We also establish Landis type results for global solutions.