Space-like quantitative uniqueness for parabolic operators

Vedansh Arya; Agnid Banerjee

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arXiv · 2207.00578

Space-like quantitative uniqueness for parabolic operators

Vedansh Arya·Agnid Banerjee

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Abstract

We obtain sharp maximal vanishing order at a given time level for solutions to parabolic equations with a $C{^1}$ potential $V$. Our main result Theorem 1.1 is a parabolic generalization of a well known result of Donnelly-Fefferman and Bakri. It also sharpens a previous result of Zhu that establishes similar vanishing order estimates which are instead averaged over time. The principal tool in our analysis is a new quantitative version of the well-known Escauriaza-Fernandez-Vessella type Carleman estimate that we establish in our setting.

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Vedansh Arya, Agnid Banerjee. 2022-07-01. Space-like quantitative uniqueness for parabolic operators. https://arxiv.org/abs/2207.00578

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