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arXiv · 2405.13253

Sharp order of vanishing for parabolic equations, nodal set estimates and Landis type results

Vedansh Arya·Agnid Banerjee·Nicola Garofalo
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Abstract

We establish a new sharp estimate of the order of 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.

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Vedansh Arya, Agnid Banerjee, Nicola Garofalo. 2024-05-21. Sharp order of vanishing for parabolic equations, nodal set estimates and Landis type results. https://arxiv.org/abs/2405.13253

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