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arXiv · 2608.27544

Quantitative Uniqueness and Rough Damping on $\mathbb T^2$

Benjamin Jaye·Rahul Sethi
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Abstract

Motivated by a conjecture of Burq and G\'erard, we investigate quantitative uniqueness principles for functions on $\mathbb T^2$ whose Fourier spectra lie in fixed-width annuli. We obtain observability estimates uniform in the radius, under a mild Sobolev regularity condition, and the generalized geometric control condition (GGCC) on the damping function. This leads to exponential decay for the damped wave equation with rough damping. We also establish an analogous uncertainty principle for spectra near dilates of convex polygonal boundaries, where no Sobolev regularity of the damping is required beyond $L^\infty$.

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Benjamin Jaye, Rahul Sethi. 2026-08-27. Quantitative Uniqueness and Rough Damping on $\mathbb T^2$. https://arxiv.org/abs/2608.27544

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