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arXiv · 2401.17782

Unique continuation estimates for Baouendi--Grushin equations on cylinders

Paul Alphonse·Albrecht Seelmann
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Abstract

We prove time-pointwise quantitative unique continuation estimates for the evolution operators associated to (fractional powers of) the Baouendi--Grushin operators on the cylinder $\mathbb{R}^d \times \mathbb{T}^d$. Corresponding spectral inequalities, relating for functions from spectral subspaces associated to finite energy intervals their $L^2$-norm on the whole cylinder to the $L^2$-norm on a suitable subset, and results on exact and approximate null-controllabilty are deduced. This extends and complements results obtained recently by the authors and by Jaming and Wang.

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Paul Alphonse, Albrecht Seelmann. 2024-01-31. Unique continuation estimates for Baouendi--Grushin equations on cylinders. https://doi.org/10.2140/paa.2025.7.733

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